From ff7602121d0535aed903988c5082d24a779146d8 Mon Sep 17 00:00:00 2001 From: AAT Date: Sat, 9 Dec 2017 05:11:42 +0530 Subject: [PATCH 01/13] Temporary commit --- .gitignore | 1 + dg_maxwell/__init__.py | 3 +- dg_maxwell/isoparam.py | 4 +- dg_maxwell/lagrange.py | 3 +- dg_maxwell/msh_parser.py | 3 +- dg_maxwell/params.py | 14 +- dg_maxwell/tests/convergence_tests.py | 4 +- dg_maxwell/tests/isoparam/test_isoparam.py | 4 +- .../tests/msh_parser/test_msh_parser.py | 3 +- dg_maxwell/tests/test_waveEqn.py | 62 ++++- dg_maxwell/utils.py | 3 +- dg_maxwell/wave_equation.py | 97 ++++++- .../maxwell's_equations_1d.ipynb | 237 ++++++++++++++++++ .../read_and_plot_mesh.ipynb | 12 + main.py | 6 +- 15 files changed, 439 insertions(+), 17 deletions(-) create mode 100644 examples/maxwells_equations/maxwell's_equations_1d.ipynb diff --git a/.gitignore b/.gitignore index d8b3dc5..0edc383 100644 --- a/.gitignore +++ b/.gitignore @@ -197,4 +197,5 @@ Thumbs.db !examples/read_and_plot_mesh/mesh/* !dg_maxwell/tests/mesh/* !dg_maxwell/tests/msh_parser/mesh/* +!examples/maxwells_equations/* !docs/quazar_logo.png diff --git a/dg_maxwell/__init__.py b/dg_maxwell/__init__.py index ac983a9..73cf99f 100644 --- a/dg_maxwell/__init__.py +++ b/dg_maxwell/__init__.py @@ -2,6 +2,7 @@ # -*- coding: utf-8 -*- import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) from dg_maxwell import params diff --git a/dg_maxwell/isoparam.py b/dg_maxwell/isoparam.py index c16b337..5579701 100644 --- a/dg_maxwell/isoparam.py +++ b/dg_maxwell/isoparam.py @@ -2,7 +2,9 @@ # -*- coding: utf-8 -*- import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) + from dg_maxwell import utils def isoparam_1D(x_nodes, xi): diff --git a/dg_maxwell/lagrange.py b/dg_maxwell/lagrange.py index 0bc2185..2029de2 100644 --- a/dg_maxwell/lagrange.py +++ b/dg_maxwell/lagrange.py @@ -4,7 +4,8 @@ import numpy as np from scipy import special as sp import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) from dg_maxwell import utils from dg_maxwell import params diff --git a/dg_maxwell/msh_parser.py b/dg_maxwell/msh_parser.py index 00c74ae..b91fb3f 100644 --- a/dg_maxwell/msh_parser.py +++ b/dg_maxwell/msh_parser.py @@ -5,7 +5,8 @@ import matplotlib.lines as lines import gmshtranslator.gmshtranslator as gmsh import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) from dg_maxwell import msh_parser from dg_maxwell import isoparam diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index 0f55a6f..731e4d6 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -3,7 +3,8 @@ import numpy as np import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) from dg_maxwell import lagrange from dg_maxwell import utils @@ -83,13 +84,14 @@ af.sum(x_nodes[1] - element_size), N_Elements) np_element_array = np.concatenate((af.transpose(elements), - af.transpose(elements + element_size))) + af.transpose(elements + element_size))) element_mesh_nodes = utils.linspace(af.sum(x_nodes[0]), - af.sum(x_nodes[1]), N_Elements + 1) + af.sum(x_nodes[1]), + N_Elements + 1) element_array = af.transpose(af.interop.np_to_af_array(np_element_array)) -element_LGL = wave_equation.mapping_xi_to_x(af.transpose(element_array),\ - xi_LGL) +element_LGL = wave_equation.mapping_xi_to_x(af.transpose(element_array), + xi_LGL) # The minimum distance between 2 mapped LGL points. delta_x = af.min((element_LGL - af.shift(element_LGL, 1, 0))[1:, :]) @@ -104,7 +106,7 @@ # Array of timesteps seperated by delta_t. time = utils.linspace(0, int(total_time / delta_t) * delta_t, - int(total_time / delta_t)) + int(total_time / delta_t)) # The wave to be advected is either a sin or a Gaussian wave. diff --git a/dg_maxwell/tests/convergence_tests.py b/dg_maxwell/tests/convergence_tests.py index 87abd62..04b5953 100644 --- a/dg_maxwell/tests/convergence_tests.py +++ b/dg_maxwell/tests/convergence_tests.py @@ -1,7 +1,9 @@ from dg_maxwell import params from dg_maxwell import wave_equation - +import arrayfire as af +af.set_backend('opencl') +af.set_device(0) def L1_norm(u): ''' diff --git a/dg_maxwell/tests/isoparam/test_isoparam.py b/dg_maxwell/tests/isoparam/test_isoparam.py index beef0bd..cfa2bee 100644 --- a/dg_maxwell/tests/isoparam/test_isoparam.py +++ b/dg_maxwell/tests/isoparam/test_isoparam.py @@ -6,7 +6,9 @@ sys.path.insert(0, os.path.abspath('./')) import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) + import numpy as np from dg_maxwell import isoparam diff --git a/dg_maxwell/tests/msh_parser/test_msh_parser.py b/dg_maxwell/tests/msh_parser/test_msh_parser.py index c77deb7..11ab2e4 100644 --- a/dg_maxwell/tests/msh_parser/test_msh_parser.py +++ b/dg_maxwell/tests/msh_parser/test_msh_parser.py @@ -6,7 +6,8 @@ sys.path.insert(0, os.path.abspath('./')) import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) import numpy as np diff --git a/dg_maxwell/tests/test_waveEqn.py b/dg_maxwell/tests/test_waveEqn.py index fca055b..d0c2c76 100644 --- a/dg_maxwell/tests/test_waveEqn.py +++ b/dg_maxwell/tests/test_waveEqn.py @@ -7,7 +7,8 @@ import numpy as np import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) from dg_maxwell import params from dg_maxwell import lagrange @@ -373,6 +374,65 @@ def test_volume_integral_flux(): numerical_flux = wave_equation.volume_integral_flux(params.u[:, :, 0]) assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) + +def test_volume_integral_flux_u_n_flux_n(): + ''' + A test function to check the volume_integral_flux function in wave_equation + module by analytically calculated Gauss-Lobatto quadrature. + + Reference + --------- + The link to the sage worksheet where the calculations were caried out is + given below. + `https://goo.gl/5Mub8M` + ''' + threshold = 4e-9 + params.c = 1 + change_parameters(8, 10, 11, 'gaussian') + + referenceFluxIntegral = af.transpose(af.interop.np_to_af_array(np.array + ([ + [-0.002016634876668093, -0.000588597708116113, -0.0013016773719126333,\ + -0.002368387579324652, -0.003620502047659841, -0.004320197094090966, + -0.003445512010153811, 0.0176615086879261],\ + + [-0.018969769374, -0.00431252844519,-0.00882630935977,-0.0144355176966,\ + -0.019612124119, -0.0209837936827, -0.0154359890788, 0.102576031756], \ + + [-0.108222418798, -0.0179274222595, -0.0337807018822, -0.0492589052599,\ + -0.0588472807471, -0.0557970236273, -0.0374764132459, 0.361310165819],\ + + [-0.374448714304, -0.0399576371245, -0.0683852285846, -0.0869229749357,\ + -0.0884322503841, -0.0714664112839, -0.0422339853622, 0.771847201979], \ + + [-0.785754362849, -0.0396035640187, -0.0579313769517, -0.0569022801117,\ + -0.0392041960688, -0.0172295769141, -0.00337464521455, 1.00000000213],\ + + [-1.00000000213, 0.00337464521455, 0.0172295769141, 0.0392041960688,\ + 0.0569022801117, 0.0579313769517, 0.0396035640187, 0.785754362849],\ + + [-0.771847201979, 0.0422339853622, 0.0714664112839, 0.0884322503841, \ + 0.0869229749357, 0.0683852285846, 0.0399576371245, 0.374448714304],\ + + [-0.361310165819, 0.0374764132459, 0.0557970236273, 0.0588472807471,\ + 0.0492589052599, 0.0337807018822, 0.0179274222595, 0.108222418798], \ + + [-0.102576031756, 0.0154359890788, 0.0209837936827, 0.019612124119, \ + 0.0144355176966, 0.00882630935977, 0.00431252844519, 0.018969769374],\ + + [-0.0176615086879, 0.00344551201015 ,0.00432019709409, 0.00362050204766,\ + 0.00236838757932, 0.00130167737191, 0.000588597708116, 0.00201663487667]\ + + ]))) + + numerical_flux = wave_equation.volume_integral_flux_u_n_flux_n( + params.u[:, :, 0], + wave_equation.flux_x(params.u[:, :, 0])) + + assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) + + + def test_lax_friedrichs_flux(): ''' A test function to test the lax_friedrichs_flux function in wave_equation diff --git a/dg_maxwell/utils.py b/dg_maxwell/utils.py index 2c6d6df..45880c8 100644 --- a/dg_maxwell/utils.py +++ b/dg_maxwell/utils.py @@ -4,7 +4,8 @@ import numpy as np import matplotlib.lines as lines import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) def add(a, b): ''' diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index c83cc23..d0cd674 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -4,7 +4,9 @@ import os import arrayfire as af -af.set_backend('cpu') +af.set_backend('opencl') +af.set_device(0) + import numpy as np from matplotlib import pyplot as plt from tqdm import trange @@ -290,6 +292,98 @@ def volume_integral_flux(u_n): return flux_integral +def volume_integral_flux_u_n_flux_n(u_n, flux_n): + ''' + + Calculates the volume integral of flux in the wave equation. + + :math:`\\int_{-1}^1 f(u) \\frac{d L_p}{d\\xi} d\\xi` + + This will give N values of flux integral as p varies from 0 to N - 1. + + This integral is carried out using the analytical form of the integrand + obtained as a linear combination of Lagrange basis polynomials. + + This integrand is the used in the integrate() function. + + Calculation of volume integral flux using N_LGL Lobatto quadrature points + can be vectorized and is much faster. + + Parameters + ---------- + + u : arrayfire.Array [N_LGL N_Elements 1 1] + Amplitude of the wave at the mapped LGL nodes of each element. + + flux_n : arrayfire:Array [N_LGL N_Elements 1 1] + Flux of the wave at the mapped LGL nodes of each element. + + Returns + ------- + + flux_integral : arrayfire.Array [N_LGL N_Elements 1 1] + Value of the volume integral flux. It contains the integral + of all N_LGL * N_Element integrands. + + ''' + # The coefficients of dLp / d\xi + diff_lag_coeff = params.dl_dxi_coeffs + + lobatto_nodes = params.lobatto_quadrature_nodes + Lobatto_weights = params.lobatto_weights_quadrature + + nodes_tile = af.transpose(af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1])) + power = af.flip(af.range(diff_lag_coeff.shape[1])) + power_tile = af.tile(power, 1, params.N_quad) + nodes_power = nodes_tile ** power_tile + weights_tile = af.transpose(af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1])) + nodes_weight = nodes_power * weights_tile + + dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight) + + + # The first option to calculate the volume integral term, directly uses + # the Lobatto quadrature instead of using the integrate() function by + # passing the coefficients of the Lagrange interpolated polynomial. + if(params.volume_integral_scheme == 'lobatto_quadrature' \ + and params.N_quad == params.N_LGL): + + # Flux using u_n, reordered to 1 X N_LGL X N_Elements array. + F_u_n = af.reorder(flux_n, 2, 0, 1) + + # Multiplying with dLp / d\xi + integral_expansion = af.broadcast(utils.multiply, + dLp_dxi, F_u_n) + + # Using the quadrature rule. + flux_integral = af.sum(integral_expansion, 1) + flux_integral = af.reorder(flux_integral, 0, 2, 1) + + # Using the integrate() function to calculate the volume integral term + # by passing the Lagrange interpolated polynomial. + else: + #print('option3') + analytical_flux_coeffs = lagrange.lagrange_interpolation_u(flux_n) + + analytical_flux_coeffs = af.reorder(analytical_flux_coeffs, 1, 0, 2) + + dl_dxi_coefficients = af.reorder(params.dl_dxi_coeffs, 1, 0) + + # The product of polynomials is calculated using af.convolve1 + volume_int_coeffs = af.convolve1(dl_dxi_coefficients, + analytical_flux_coeffs, + conv_mode=af.CONV_MODE.EXPAND) + volume_int_coeffs = af.reorder(volume_int_coeffs, 1, 2, 0) + volume_int_coeffs = af.moddims(volume_int_coeffs, + params.N_LGL * params.N_Elements, + 2 * params.N_LGL - 2) + + flux_integral = lagrange.integrate(volume_int_coeffs) + flux_integral = af.moddims(flux_integral, params.N_LGL, params.N_Elements) + + + return flux_integral + def lax_friedrichs_flux(u_n): ''' @@ -416,6 +510,7 @@ def b_vector(u_n): ''' volume_integral = volume_integral_flux(u_n) + #volume_integral = volume_integral_flux_u_n_flux_n(u_n, flux_x(u_n)) Surface_term = surface_term(u_n) b_vector_array = (volume_integral - Surface_term) diff --git a/examples/maxwells_equations/maxwell's_equations_1d.ipynb b/examples/maxwells_equations/maxwell's_equations_1d.ipynb new file mode 100644 index 0000000..f69c9f6 --- /dev/null +++ b/examples/maxwells_equations/maxwell's_equations_1d.ipynb @@ -0,0 +1,237 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../../'))\n", + "\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "import arrayfire as af\n", + "\n", + "from dg_maxwell import params\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import wave_equation as w1d\n", + "\n", + "af.set_backend('opencl')\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Set the initial conditions\n", + "\n", + "E_00 = 1.\n", + "E_01 = 1.\n", + "\n", + "B_00 = 0.2\n", + "B_01 = 0.5\n", + "\n", + "E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + E_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + B_01 * af.cos(2 * np.pi * params.element_LGL)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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XtASAtyoBtAMo0r/SAZRJKTd5k1AgIiIiIiIiCjYRu1JBCFEMYDuAagAV0FYZ+EKJlNLq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ycc4O2fMqT6HYZkp+Dx2azaW2c2m4SHD34PG57ouVqalm860Wnz+uzug9u5OriJhK9zvgoTrgef\nB57+DBf0bwecgndrpwreMc/rgUVfhLrdkDEIrn8YXJH71m1zeSNN7R4ykuKYWJhpOo4EWeR+Z4qI\nnIrpt8PMLwI2LPoiNxQ6Qxr1REjYtBDe/KHz4/k/hmHnm83TS1vLG2lo6yI9MY7JOriJhC/Lgmse\nhP6ToKWawtfvYFSWRZdXBe+YZ9vw8teh+A2IS4ab/gEpkT0fJ9D6cPaIHNwuy3AaCTYVFUQkdlz6\nCxh+AXS1cGfpD8ihQTvBY92ed+C5Lzk/PuvLPRtDIth7/q0PZ43IJs6tl3mRsJaQCrc+Aal5WBWb\n+HXCH7Hw6bUp1r39M2c4Y+D23KAzTCfqtZ6NRLpBF4102hCR2OGOd4ZjZY8gpa2cPyX8H3sr66hq\najedTEw4uBGevA18XTDhOrjkZ86TwwgXeDOig5tIhMgaDDc/Du4EJjYu51txC3WLLpZ99FdY/oDz\n4yv/D8ZebjZPELR1elldcgjQa1O0UlFBRGJLSjbc+hQkZjLTtZOfxT/C+3oiFHsO7YPHF0Bnk7N2\n9LqHIrpXNaCt08uqEufa9KyiPMNpROSkDTkLrvotAF+Le57RVa9T3dRhOJT0uW0v92x6uOB7cMbn\njMYJllUldXR6fAzMTGJkXqrpOBICkX+CEhE5VXmj4ca/4cPFAvdy3CsfNJ1I+lJrHTx2AzRXQv4E\nuOVxiEs0nSoodHATiWBTb4Xzvg7AL+MfZtvqpYYDSZ/a/yEsugNsH0z/LMz5nulEQbNiZzXgFLut\nKLgRKJ+kooKIxKZRc9l7hjOc74rKP2Fve9lwIOkTna3wr5ugthgyB8NtCyEpeoYZ6uAmEuHm3kdx\n1vkkWl1Mff8e51aVRL/qHfCvm53VkaMvgyt+FRXteAEr/DdCZ41W60O0UlFBRGJW4SXf4AnfPFzY\n2Au/ACXvmo4koeT1wMIvQOlqSMqC2xZBxkDTqYJKBzeRCOdyUzX/Qbb5BpPhqcP+53XQXG06lYRS\n40Hn9lx7PQya6QxmdMeZThU0lY3t7KhswrLgvJF6bYpWKiqISMxKSojj1cHfYrH3DFzeDnjiVji4\nwXQsCQXbhle+BTtfg7gk+NRTkDfGdKqg0sFNJDpMLxrCXd7vU2rnYtXthseuh/ZG07EkFNobnPk+\nDQcgZ5Qz8ykhxXSqoAoUuycXZtIvNcFwGgkVFRVEJKadWzSAr3Z9jR1Jk6Gj0XlaULvbdCwJtmX3\nw9q/O+u5bngEhpxtOlHQ6eAmEh2SE9wMHjaS2zq/T1t8P6jY6BS9u7SpKKp4OuDJT0PlZkjrD7c9\nC6k5plMF3YrinrY8iV4qKohITJtVlEsHCdze+k18/SdBSzX841poLDcdTYJlzaPwzs+dH1/+PzDu\nSqNxQkUHN5HoMasojxK7gAfyfgYJ6bDvXad9y+sxHU2CweeD5+6GkhXO/76fXgj9hppOFXQ+n929\n5nhWkW7QRTMVFUQkpo0vyCA3LYHKzkTWzf4LZI+Ahv3wz+udLQES2Xa8Bi9/0/nx7O/AzDvM5gkR\nn8/uvqkwe7SKCiKRbrZ/LsrTpdl03fQvcCfCjlfgpX9z2rkkctk2vPlD2PIcuOLhlsegYLLpVCGx\n9WAjtS2dpCa4mT60n+k4EkIqKohITHO5LM4f5Rzelh4APvM8pBdA9TZnS0Bni9mAcvoOrIZnPu+s\n55p2G1z4Q9OJQmbrwUbq/Ae3aUOyTMcRkV4aN8ApeLd0evnImgA3/s1p31r/OCz+f6bjSW+8/zv4\n8A/Oj6/7E4yYYzJNSAWK3eeMzCXerbed0Uz/64pIzAs82V1RXONcP7ztWWc7QOlqePp28HQaTiin\nrKbYKQp52qDoYrjy11G1nutIy/2tDzq4iUQHl8vqbmVaUVwNY6+Aq3/n/Ob7v4N3f20wnZy2jU/3\nFIUu/glMWmA2T4gF2vJmayNR1NPJQ0Ri3vn+Pr/N5Q3UNndA//Hw6WcgPgV2LYHnv+T0P0pkaKpw\n2lfa6qDwDLjxUXDHm04VUit2BlofdHATiRaBHvRA0ZBptzlvRAGW3Adr/m4omZyW3W/D819xfnz2\nPXDu18zmCbHWTg8flRwCNOsnFqioICIxLz89iXEFGdg2vLvLeXPG4DPh5n86/Y6bF8Fr96qPNRK0\nN8JjC5y5GNkj4VNPQ0Kq6VQh1drp4aN9zvwPHdxEokfg/583lzU6BW9w3oie758T8/I3YOuLhtLJ\nKTm4AZ66DXxdMPGGnuJQFFu5p45Or49B/ZIZlhNdazLlk1RUEBGh5wnvcv8TXwBGzXP6HbFg9Z/h\nnV+YCScnx9PpHNoqN0FqPty2CFKj/8n9yj11dHltHdxEokxeeiLjCzKAwwreAHPvg+m3O/NiFt0B\ne5YZSign5VCJU+zubIZhs+DaP4Ir+t+CLT9sI5EVxe2H4oj+72gRkZMw+7DeVfvwGwmTFsDlv3R+\nvOwXsPIhA+nkhHw+eP7LsHcZJKQ57SvZw02n6hM6uIlEr1n+gveyndU9v2hZzpyYcVeBtxOe/BSU\nrTWUUI6rpcZpx2upgv4T4ZbHIS7RdKo+0b2RSKskY4KKCiIiwIxh/UiKd1HV1MGOyqaP/+aZd8Kc\nHzg/fu1eZ9CShJfF/w82LwRXnNO2MnCq6UR9Rgc3keh1QVHPIOGPFbxdbrjhERh+gfME/PEFUL3T\nUEo5qs4WZ2Bw3W7IHAKfXghJmaZT9Yny+jZ2VTXjsuDckXptigUqKoiIAIlxbs4ekQPA8sOfCAVc\ncC+cebfz4+e/DBuf6cN0clzv/w4+eND58TV/gJEXmc3Th3RwE4luZwzrR3K8m+qmDrZXHFHwjkt0\nnnwPnAattfCPa6Byq5mg8nGeTmelcdkaSO7ntONlFJhO1Wfe9Re7pwzOIjMlugcli0NFBRERv9mH\nPRH6BMuCS38Bk28Gnwee/SIse0DDG03y+WDxj+DN/3B+Pv/HMOVms5n6mA5uItHNKXhnAz3r+T7+\nB9Lh04sgdww0lcNfL4FdS/s4pXxMax08dj0UvwFxyc7A4LzRplP1qcPb8iQ2qKggIuI3e7Tz4rdy\nbx1tnd5P/gGXC679U88aqLd/6qyH8nT2YUoBoLMVnrkd3vuN8/M534dz/81sJgN0cBOJfoHXpo8N\nEj5cag584XUYeh50NMLjN8KaR/suoPSo3Q2PzIeSFZCQ7twkGXym6VR9yuuzuweLqi0vdqioICLi\nNzIvlYGZSXR6fKzcW3v0P+RyOaugrvgVWG7Y8C/niUTbob4NG8uaKuDRy2HbS+BOgOv/DHO+59wm\niSE6uInEhkDRcFXJMQreACnZ8JnnnNt0thde+josvs+50SV9o+Q9+MtcqN0FmYPhjjdg1FzTqfrc\nlvIG6lu7SE+MY8rgLNNxpI+oqCAi4mdZVvcToaO2QBxu5h3OlcaEdOeJxF/mQ93ePkgZ4yo2wZ8v\ngvJ1kJwNt78Ik28yncqIzWU6uInEgpF5qRRmJR+/4A3OjIXrHnJubgG892tY+DnoauuTnDFt/RPO\nTIu2QzBwOnxxKfSfYDqVEYHz0zkjc4h3661mrND/0iIihwk8ETrqsMYjFc1zrpxmFEJtsfOE4sCq\nECeMYTvfgL9eCo1lkFMEdy6FoeeYTmVMoL9aBzeR6GZZFrP8t5GO2QLR84edm1vXPQSueNj6Ajx6\nJTSfxGuanDqfD976CTz/JfB1wfhr4HOvQHp/08mMCZyfZo1WW14s0SlEROQw543KwWVBcVUz5fUn\n8XRnwETniUTBFGf69qNXwuZnQx801qx8CJ64xVmdNnw2fHExZI8wncqo5YFVkjq4iUS97rkKRxvW\neDRTboHbn4ekLCj7yCl6V+8IYcIY1NUGi+6A5b90fn7+t2DBo5CQYjSWSc0dHtbud9pBL9Csn5ii\nooKIyGGyUhKYPMi5Sv7uiVogAjIK4POvwejLwNsBCz8PK36lzRDB4PXAq9+B1+4F2wfTPgO3Peus\n6IphzR0e1u5zDm6zdXATiXrnjczFZcGuky14Aww7H764BPoNg/p9zgDBvctDmjNmNFfD36+CLc86\nN0Ku+T3Mu8+ZuxTDVu6ppctrMzQnhSE5sVtciUWx/Z0vInIUgSdCy072iRBAQqoz5fmsLzs/X/pf\n8NK/gbcrBAljRHujczth1cPOz+f/GK7+Hbi1OvHD3bV4fDq4icSKzJT47tkpR10teSy5Rc5tusFn\nQXsD/PM6WPd4iFLGiKpt8JeLoHS1cxPkM8/BtNtMpwoLgXkKszQ8OOaoqCAicoQLRjsvhu/tqsHr\nO4XbBi43XPYLuOwBsFyw9h/w+ALnICenpv6AMz9h12Jnz/dN/4Tzvh5zGx6OZUX3Kkkd3ERiReBW\n0vKTvUUXkJrrDLWdcD34PPDCV5w5ALpNd+p2LYVHLob6/dBvuHMTZPgs06nChtYcxy4VFUREjjBl\nUBbpSXHUt3axqew0CgJn3Q23PAHxqbDnnZ4DiJyc0jXOhoeqLZDWHz7/Koy/2nSqsNLzNEgHN5FY\nMdtf8H63+BQL3gDxSXDDIzDr287Pl/8SFn0RutqDnDKKrX4EHr8ROhphyLnODZDcItOpwkbpoVb2\nVLfgdlmcMzLHdBzpYyoqiIgcIc7t4ryRgUnbpzkxe8yl8IXXIL0AqrfDn+dC2ZogpoxSW56HRy+H\nliroPxHufAsKp5tOFVYO1LWyp0YHN5FYEyh4N7R1sbG0/tQ/gcsFc38EVz8IrjjYvBD+eS20HGdN\npYDPC6//AF75FthemHKrMwQzVX//Hi4wh2ra4CwyktSmGGtUVBAROYpZ/idCp9S7eqSCKf5d1ZOc\nN8l/uwK2vRSkhFHGtp3hls98FjztUHSJs64zc5DpZGHn3V06uInEosML3itOtQXicNM/A7ctgsRM\n2P8BPDIPancHKWWU6WiGp26DD3/v/Pyi/4Br/whxiWZzhSG1PsQ2FRVERI4i0Lu6dn89je29GLaY\nWejcWBg1Hzxt8NRn4P0H1ct6OE8nvPBVZ7glwFlfglufgMR0s7nC1Aod3ERiVvdqydO9RRcwYg7c\n8SZkDYG6Pc7KyX3v9zpfVGkog79dCjteBXciLPgrzP6OZvschddnd99UCDyUkdiiokKQWJY1wrIs\n3dEViRKDs1MYkZuK12fz/q5eXg1NTIdbn4QZdwA2vPlDeOx6OLgxKFkjWu1u5/rt+sec4ZaX/RIu\nu98ZeimfoIObSGwLDGddd6CXBW+A/LHObbrCM6DtkLMi8dXvOOsSY92uJU6hpWITpOTC516GiTeY\nThW2NpbW09juISMpjsmFmabjiAExXVSwLCvLsqz7/R/3Wpb1kGVZd53mp1sArLEs65BlWYsty3rG\n/8/d/n9mBTO7iIRe4PDWqxaIAHccXPG/cMnPnF7W3W/BQ7Ng0Z1waF/vP3+k6WiGJf8Jfzgb9r0H\nCenwqafhrNP9Kzg26OAmEtuCWvAGSMuHz77csxli1cPw26nwzv3O39Oxpm4vPPEpeOwGaDoIeWPh\nzqUw+EzTycJaoB3nvFG5xLlj+u1lzIrZ/9X9b/LXAE/Ztv1d27YfsG37bmCkZVkPneanXQLUAfP8\nH9nA/bZtz7dt+zQm6oiISd3XTIursYPRrmBZcM498NXVPU88Nj0ND86A178fG8OybBs2LYQHZ8K7\n/wfeThg1D+5eBkXzTacLe8t36uAmEusOf20KioQUuPFvcPsLUDAVOpvhnZ/Bb6fB6r+At5c3IiJB\nZyu89VP4/Vmw4xWn+H/2PXDHYug3zHS6sKe2PInlE8kzwELbttce/ou2bX8XuMmyrHmn8Tnvtm17\npG3blm3b/WzbPsO27YeDklZE+tzZI3KId1scqGtjX21r8D5x9ginN/Oud2D4Bc4b6w//4DwdWv4/\n0NkSvK8VTio2waNXwKI7oKncOajd+iR8eiHkjDSdLiLo4CYigVt0y3cGqeAdMGIO3Pm28/rUb5gz\nYPiVbztvtLc8H52zgGwbtjznFLqXPwDeDuf/Dl96Dy79GSRlmE4Y9prau1i733l2GvjelNgTk0UF\ny7JG4NwkONaNhKeB+/sukYiEo9TEOM4Y2g8I4hOhww2c5jwZuu1ZGDDJ2X391n/Db6fDR38Dryf4\nX7xY3CYAACAASURBVNOE1jp45d/hodlOq0N8ijNB+ysrYcxlGnp1khrbu1h3QAc3kVgXKHiXHmqj\nJJgFb3DWTk68Ae5Z7cy4ScmFut3OZp6/zIW9K4L79Uyq2gb/uBqe+Rw0lkLmELjpn/CZ5515E3JS\nPthdi9dnMzw3lcHZKabjiCExWVTAmX+Abdt7jvH7u4Hp4TYHobGx8aQ+Ojo6TEcViRpBm7R9LJYF\no+bCXcvh+r84k7ibK+DlbzjzBra9FLlPh3xe+Oiv8LszYPWfwfbBhOuc9o/Z34H4JNMJI4oObiIC\nTsF7xtBsIISvTXEJzoybr6+HC74H8alQtgb+fiU8tgAqNofm6/aFtnp47Xvwx/Ng73KIS3L+G+9Z\nCeOvVqH7FAXmKajYHdtitagwHzjejINAsWFGH2Q5aQMHDiQzM/OEHz//+c9NRxWJGoHVkh/srqXT\n4wvdF3K5YPKN8NWP4NJfQHI21BY7+7EfuRj2fRC6rx0K+1fCny+El78JbXWQPx4++xLc+ChkDjKd\nLiL1tD7o4CYS6wLbX4IySPh4EtPhwu87xYWZX3RmDexaDH86H577EtQfCO3XDyafD9b+0yl0r/wj\n2F4YdxXcs8r5b0xQsfZ0qC1PAOJMBzAkG2eg4rEECg4jTvUTW5a14Mh/z7btB0718xxNeXk5qamp\nJ/xziYmJwfhyIgKML8ggJzWB2pZO1u4/xNkjckL7BeMS4ewvw9RPwfu/gw9+D6WrnF3Zoy+DefdB\n/rjQZjhdtg0HVjmHtS3POb+WlAkX/tBZp+mO1Zec4Ag8DZqtg5tIzJtdlMcDr+/oLngnxIX4OWFa\nvrPB6OyvOG16W56DDU/A5mfhzDth1rchJTu0GU6XpxO2v+S8ppavc34td7SzvnjkRWazRbj9ta2U\n1LYS57I4Z2SIz0cS1mL1hHeitoZAweFU2x/uBn5++KYH/6rKxbZt93qseUZGxkkVFUQkeFwui/OL\ncnlhfTkriqtDX1QISMp05g7M/CK88wtY+w/Y+RoUv+EUHOb8ADIL+ybLiXQ0w6ZnYPUjULnJ/4sW\nTP8MzL0PUvVkvbf21bawz39wO1sHN5GY1+cF74Cckc6Ns3O/Bovvg5IV8MGDzg2AWd+Es74E8cl9\nk+VEGkphzaOw5u/O0Elw1hfP+R6cdTe4443GiwYrdjm3FKYP7UdaYqy+rRSI3aJCNj0tDsdzKn9D\nLzzajAbbth+wLOv7lmXdG6wbCyLSt2YX5fHC+nKW76zhO5f08RdPHwBX/dpZRbn0x7DtRVj3mLOW\ncfrtMOQcGDDZ2Sjh6sOONq8HDnwIW1+ADU86QybB6U2dtMA5WA6Y1Hd5olzgloIObiICTsF7VlEu\nz68vZ/nOPix4BxSe4bS07VoKS+6Dys2w5D9h5cMw4wvOIOIBkyC9f9/mam+E3W/BxqedQrztb1tM\nGwBnfA5m3uHcupCgWLEzcINODw9iXayeTII+gPE4Qx8BluBsk1BRQSQCBXrYN5c3UNvcQU6agRaj\n3CK4+Z9wYDUs/hHsfx9WPex8gDNEq/8E5xA3YJJTaMgfF9we0bZ62LUEdr4OxYuh/bDRNNkjnFsV\nUz8Fyf2C9zUF6OlZ1cFNRAJmj85zigrF1dx7qYFtBZYFRfOcFoJNT8NbP4GGA/D2T3r+TGrex1+X\nBkyCnFHgcgcvx6F9zuvSjteg5F3wdfX83rBZzmvT2Ct0MyHIPF4f7+0ODGlUW16sC/uign8Dwwic\n2wWno8627bVH/Fo9J1dYqD3Nr3mkPQCWZU0/ShYRCXP5GUmMHZDO9oom3t1VwzVTDbYdDJ4Jn3/V\neVO//WWo2ARVW6GrxZm9ULqq589aLsgpOuxAN9E51B3rKU1XOzSWOR8NpdBQ5hwQAz+v3QW+w9Zc\nJmdD0cUw5WYYPqdvb0rEEI/Xx/u7nJcjHdxEJOD8QMG7rNFcwRucv/un3ALjr4X1jzurgys2QU0x\ntFQ7Nwd2v9Xz5+OSof9453Wpv/91qf8ESEw7+udvb3Regxr9r0kNZT0/r98H9fs//uezRzrriqd9\nRqshQ2hDaQNN7R6yUuKZWJhpOo4YFvZFBeAunFkFvTHyiJ8fb0gj9BQwjrch4lTs9v9zBqCigkgE\numB0Htsrmli+03BRAZynQ6Mvdj7AaUWo2+0c4io2Ov88uBFaa6Bmh/OxeWHPv5/W3znMZQ2F5sqe\nokHLSUwRzx0DY/xDIwefGdynTXJUG0rraerQwU1EPi4/PYlxBRlsO9hovuANzprgmXc4HwCdLVC1\nzf/a5P+o3Axdrc56yrI1h/3LlnPjbcAkSM5yCgeB16ZAe92xWG4YcjaMvtQpJuQWhew/UXoEbtCd\nNyoXt0trOGNd2BcV/HMIgt02sBZYcJzfD9xiOJm5C1iW9RAwz7btI4sXRzpRMUNEwtSsojweWr6H\nFcXV2LaNFU57rN1xkDfG+Zjk/6vNtp2CweGFhorNzm2D5krYVXn0zxWX7Kx8zCx0/pkxqOfnOaMg\na0jf/XcJAMt2+A9uI3VwE5GPm12Uy7aDjSzbWW2+qHCkhFQYNMP5CPB5oW7vYa9L/o/mCqc4Xrf7\n6J8rKQsyBx/22lTY8/O8seG7eSKKLdvpXyU5Sm15EgFFhRBZzPGLCiMAbNtecpKfbwaQbVlW1uGb\nHw4TKFLoloJIhJoxrB9J8S6qmjrYUdnE2AEZpiMdn2U5Qx7TB0DRYctnOlugcqtzoGsohfSCjxcQ\nUrKdf1fCxjv+g9sFY9T6ICIfN3t0oOBdE34F76NxuSF3lPMx8fqeX2+udrYHVWxyNgp1F7cHOwWE\nY7VGiBF1LZ2sP+C85dFrk0DsFhWWwHFnHMwM/JmT/Xy2bX/3OL9/M1B/gmGOIhLGkuLdnDU8h2U7\nq1m+szr8iwrHkpDqzGUYPNN0EjkJ1U0dbCxtAGDOaB3cROTjzhjqFLyrmzrYXtHEuIIIfW1Ky4O0\ni5yhjxL2nFubMHZAOgWZYbJCVIyKyala/jf3Szj2rIYFONsaPsayrCzLsu63LGveEb/1lGVZ9x7t\nE1mWNQKYDtzYi8giEgZm+9/UBdb7iYTacv8thQkDM8jPSDKcRkTCTVK8u3udZKDHXSTU3vG35c0Z\no/Wc4ojJooLfjcA8y7KmH/6LlmU9Azx8jNaHu4B7cdonugVuOxxZWPAXFBYD3z2FVgoRCVMXjHb6\nBlfuraOt02s4jcSCt3dUAXChDm4icgyz/Vthlu9UwVtCz+ezu+cpXKjWB/GL1fYHbNuutyzrDOB+\ny7LqcdZHjgQW27b98DH+tSU4GyGePsrne8CyrHn+oY3ZOHMU6oEbtUZSJDqMzEujIDOJgw3trNxb\nqwq9hJTH6+u+FTNHBzcROYbZ/oL3qpI6Wjs9pCTE7PFe+sDGsgbqWjpJT4xj+tB+puNImIjpv3X8\nQxVPel2lvzhwzP/v8d9G0I0EkShlWRZzxuTxxKoDvLW9SkUFCan1B+ppaOsiMzmeqYOzTvwviEhM\nGpmXRmFWMmX1bby3q5b54/ubjiRR7O3tzg26WaNziXfH8qV3OZy+E0RETsG8cc5hbcnWSmzbNpxG\nolmgZ3VWUS5xOriJyDFYltVdSFiy9RjrgkWCJLCRSA9W5HA6pYiInILzRuWSFO+ivKGdrQcbTceR\nKKZ5CiJysuaOc/6eWLq9Cp9PBW8JjZrmDjaWOqsktZFIDqeigojIKUiKd3P+KOeFdOm2KsNpJFpV\nNbazpdwpWmkHuIicyFnDc0hLjKOmuYMN/jd9IsG2fKezSlIbieRIKiqIiJyi+eOdJ0JLtumaqYRG\n4Hrp5EGZ5KYlGk4jIuEuIc7VXYDUa5OESs8qSRW75eNUVBAROUUXje2PZcHG0gYqGtpNx5EotEw7\nwEXkFM3vnvmjW3QSfF6fzfLiwCpJvTbJx6moICJyivLSE7un8S/dridCElwer6/74KanQSJysuaM\nycPtsthR2cT+2lbTcSTKrD9QT31rFxlJcdpIJJ+gooKIyGk4fAuESDCt3V9PU7uHfinxTBmkg5uI\nnJyslARmDHU2n6sFQoLtHf/w4Nmj87SRSD5B3xEiIqchUFR4b3ctrZ0ew2kkmrx92MHN7bIMpxGR\nSBJYLalbdBJs76gtT45DRQURkdMwun8ag7OT6fT4WFFcYzqORJHAwU09qyJyqub6C94r99TR0NZl\nOI1Ei6qmdjaVNQBwgVZJylGoqCAichosy1ILhARdRUM72w42YlnOTQURkVMxPDeVUflpeHw2y/xb\nZER6a/lO5+HJ5EGZ5KVrI5F8kooKIiKnKTBp+63tVXh9tuE0Eg0CPatTBmWRnZpgOI2IRCIVvCXY\nAm15c1TslmNQUUFE5DTNHJ5NelIctS2drD9QbzqORAHtABeR3po3zmmdemdHFV1en+E0Euk8Xh8r\n/Lde5oxVW54cnYoKIiKnKd7t6h5YpEnb0ludHh/v7nKumGqegoicrmlD+pGdmkBju4fVJXWm40iE\nW7PvEI3tHrK0kUiOQ0UFEZFeCDwR0jVT6a2Ve2tp7vCQl57IpMJM03FEJEK5XRYXjQ28NlUZTiOR\nbul253vowjH52kgkx6SigohIL8wZnU+cy6K4qpmSmhbTcSSCLd3mHNwuGpOPSwc3EemFwFyFxdsq\nsG3N/JHTt9R/E3PuON2gk2NTUUFEpBcyU+I5c3g2oBYIOX22bXfvldfBTUR6a1ZRLglxLg7UtVFc\n1Ww6jkSokpoWdle3EOeytJFIjktFBRGRXgrsBQ88aRY5VcVVzRyoayMhzsX5Rbmm44hIhEtNjOPc\nkTmACt5y+gKtD2cOzyYjKd5wGglnKiqIiPRSYK7CqpI6Glq7DKeRSBQoSJ07MoeUhDjDaUQkGmi1\npPRWT+tDf8NJJNypqCAi0ktDc1IZ3T8Nr8/mnZ26rSCnrvvgpnVdIhIkgVaqdQfqqW7qMJxGIk1j\nexer9jrbQ/TaJCeiooKISBB0D8XSEyE5RXUtnazdfwiAi/Q0SESCpCAzmUmFmdg2vL1dBW85Nct3\nVuPx2YzMS2VYbqrpOBLmVFQQEQmCeeOdN4PLdlTT6fEZTiOR5J0dVfhsGFeQQWFWsuk4IhJFerZA\nqOAtpybQlqfWBzkZKiqIiATB1EFZ5KYl0NThYXVJnek4EkG6D266XioiQRZogXi3uIb2Lq/hNBIp\nvD6bt3fotUlOnooKIiJB4HJZXOR/4VULhJysTo+P5TurAa2SFJHgmzAwg4LMJNq6vLy/u8Z0HIkQ\na/cfor61i8zkeM4Y2s90HIkAKiqIiARJ96TtbZXYtm04jUSC1SV1NHV4yE1LYMqgLNNxRCTKWJZ1\n2MwfzVWQkxNYQzpnTB5xbr1dlBPTd4mISJCcX5RLYpyL0kNt7KhsMh1HIkCg9eHCMfm4XJbhNCIS\njQIzf5Zuq8TnU8FbTuwtzVOQU6SigohIkKQkxHH+qFxAe8HlxGzbZul27QAXkdA6e0Q2qQluqpo6\n2FTWYDqOhLn9ta0UVzXjdllcMDrPdByJECoqiIgE0dzuFghdM5Xj213dzL7aVhLcLmYV5ZqOIyJR\nKjHOzWz/m8Ol2gIhJxBofZg5rB+ZyfGG00ikUFFBRCSIAsP21h+op6qp3XAaCWeB1oezR+aQmhhn\nOI2IRLOe1ZIqeMvxvbXd+R6Zpxt0cgpUVBARCaL+GUlMGZQJ9PQkihxNoKgwT1sfRCTELhybj8uC\nbQcbKT3UajqOhKmm9i5W7q0F1JYnp0ZFBRGRIDt8C4TI0dS3dvLRvjqA7lWkIiKhkp2awIyh2UBP\nQVPkSCuKa+jy2ozITWV4bqrpOBJBVFQQEQmywKTtFcU1tHV6DaeRcPTW9ip8NowdkM6gfimm44hI\nDJg33ilgquAtx7J4a2B4sIrdcmpUVBARCbKxA9IpzEqmw+PjvV01puNIGHp1UwUAF08YYDiJiMSK\nwHX2D/fU0tTeZTiNhJsOj7d7c9Ulem2SU6SigohIkFmW1d0nrydCcqTmDg/Li6sBuHySDm4i0jdG\n5qUxIjeVLq/N8p0qeMvHvb+rlqYOD/npiUwf0s90HIkwKiqIiIRAoAViybYqfD7bcBoJJ29vr6LT\n42N4bipj+qebjiMiMaTntUkFb/m41zYfBODSiQNwuSzDaSTSqKggIhICZw3PIS0xjprmDjaU1puO\nI2Hk8IObZengJiJ9JzBI+K3tVXi8PsNpJFx0eX286W99uHSibtDJqVNRQUQkBBLiXFwwOg/QpG3p\n0dbp5e3t/taHiQWG04hIrJk+JIuslHga2rpYs++Q6TgSJlbuqaO+tYuc1ATOHJZtOo5EIBUVRERC\nRJO25UjLdlbR1uVlUL9kJhZmmI4jIjEmzu3iojF6bZKPe9V/g+7iCf2Jc+vtoZw6fdeIiITIhWPy\ncbsstlc0caCu1XQcCQOvbXa2Plw6Qa0PImJGYK7C4q2V2LZm/sQ6r8/mzS3+1ybdoJPTpKKCiEiI\nZKUkMGOoM0FZT4Skw+PtboW5bJIObiJixuzReSS4XZTUtrK7usV0HDHso5I6apo7yUyO59yROabj\nSIRSUUFEJITma9K2+L1bXENzh4f+GYlMG5xlOo6IxKi0xDjO9r951GuTBG7QzRvXn3i1Pshp0neO\niEgIzfVP2l65p47G9i7DacSkwMHtsokFWtclIkbNG+fMVViqokJM8/lsXve/Nl0+SVsf5PSpqCAi\nEkLDc1MZmZeKx2ezbEe16ThiSJfXx2Kt6xKRMBEoeK/Zd4ja5g7DacSU9aX1VDS2k5YYx/lFuabj\nSARTUUFEJMTmqQUi5n2wu5aGti5y0xKYqXVdImJYYVYy4wsy8NnwtgreMeu1Tc7Wh4vG5pMY5zac\nRiKZigoiIiE23/9E6O3tVXR5fYbTiAmB1oeLJwzArdYHEQkD3QXvrSp4xyLbtrtfm9T6IL2looKI\nSIhNG9KP7NQEGts9rC6pMx1H+tjh67ouU+uDiISJQMF7eXE17V1ew2mkr20ua6T0UBvJ8W4uGJ1v\nOo5EOBUVRERCzO2yuHBMYChWleE00tdW7a2jtqWTrJR4zh6hdV0iEh4mFmbQPyOR1k4vH+6pNR1H\n+thrm53WhwvH5pGcoNYH6R0VFURE+sD88U5RYcm2SmzbNpxG+tLr/oPbfK3rEpEwYllW98BGzfyJ\nLYe3Plw6scBwGokGOt2IiPSBWUV5JLhd7KttZVdVs+k40kd8vp6D22XqWRWRMBNogViytUoF7xiy\no7KJvTUtJMS5uGisWh+k91RUEBHpA6mJcZw7yrn6vlhPhGLGugOHqGrqID0xjvNGaV2XiISXc0bm\nkBzvpqKxnS3ljabjSB95bZNT7J5dlEdaYpzhNBINVFQQEekj88Zp0nasedV/cJs7Tuu6RCT8JMW7\nmT3aKXgu1mtTzAjMU9DwYAkWFRVERPrI3HHOFcN1B+qpae4wnEZCzbZtXlfPqoiEucBchaXbVVSI\nBburm9lZ2Uycy+p+2CHSWyoqiIj0kYLMZCYWZmDb8Ja2QES9TWUNlNW3kZLgZs6YPNNxRESO6qKx\n+ViWs2KwvL7NdBwJsUCx+7xRuWSmxBtOI9FCRQURkT508XjnquGLG8oNJ5FQC7Q+XDgmn6R4tT6I\nSHjKTUtkxtB+ALyk16ao9+omtT5I8KmoICLSh66dWgjAe7trONigJ0LRyml98B/ctPVBRMLcddMG\nAbBobam2QESx/bWtbClvxO2yuHiCXpskeFRUEBHpQ0NyUjhzWDa2Dc+tKzMdR0Jke0UTJbWtJMa5\nuHCM1nWJSHi7YnIBCXEudlY2awtEFHt9i1PsPmt4NtmpCYbTSDRRUUFEpI/dcIZzW2HRGj0Rilav\n+a+Xzh6dR6rWdYlImMtMjmf+eGdo38I1pYbTSKgE2vLU+iDBpqKCiEgfu3xSAUnxLnZXt7CxtMF0\nHAmB1/yDsC5X64OIRIgF050WiBc3lNPl9RlOI8FWXt/G+gP1WBZcotYHCTIVFURE+lh6Unz3C/qi\ntXoiFG12VTVRXNVMvNviorFa1yUikWFWUS65aYnUtXTyzo5q03EkyAJbH2YM7Ud+RpLhNBJtVFQQ\nETHg+sOeCHV4vIbTSDC9tumwdV3JWtclIpEhzu3i2qkDAac9T6JLoKhw6cQCw0kkGqmoICJiwPmj\ncumfkUh9axdvb68yHUeCqLv1QQc3EYkwN5zhFLyXbq/kUEun4TQSLFVN7azeVwfApZqnICGgooKI\niAFul8W10/wDG9dqC0S02FfbwtaDzrquwNAzEZFIMa4gg/EFGXR5bV7eWG46jgTJG1sqsW2YMjiL\nwqxk03EkCqmoICJiyA3+Foi3t1dR29xhOI0EQ+CWwjkjcuindV0iEoECtxUWquAdNV7f7Gwkuly3\nFCREVFQQETFkdP90JhVm4vHZvLhBT4SiQWCVpK6XikikunrKQNwuiw0H6tlV1Ww6jvRSXUsnH+5x\nWh8uU1uehIiKCiIiBt0wPdACoaFYka6svo0NpQ1YFlw8Qa0PIhKZ8tITmTM6D9BrUzRYvLUCr89m\nfEEGQ3JSTMeRKKWigoiIQVdPLSTebbG5rJEdFU2m40gvBCZrzxyWTX661nWJSOQKtEA8v64Mr882\nnEZ6o3t48CTdoJPQUVFBRMSg7NQELhyTD8CzeiIU0QKtD5ep9UFEItzccflkJsdzsKGdD3bXmo4j\np6mhrYv3dtUAWiUpoaWigoiIYYEnQs+tK8Pj9RlOI6fjYEMba/YfAjRPQUQiX2Kcm6umOG9C1QIR\nuRZvraTLazO6fxqj8tNMx5EopqKCiIhhF47Jp19KPFVNHbzrf6IgkeWZj0qxbThzWDYFmVrXJSKR\n73r/hqLXN1fQ3OExnEZOx1Or9wNw1eSBhpNItFNRQUTEsIQ4F1dPcV7wn9UKr4jj89k8tfoAALee\nNdhwGhGR4Jg2OIsRuam0dXm727skcuyqamJ1ySHcLosbZ+i1SUJLRQURkTAQaIF4Y0sFje1dhtPI\nqVixq4ay+jYykuK0rktEooZlWd2vTWqBiDxPrnKK3ReOyWdApoYHS2ipqCAiEgYmFWZSlJ9Gh8fH\nqxv1RCiSPLnKuV56/fRBJMW7DacREQmea6cVYlnw4Z46DtS1mo4jJ6nD4+0uBN16pm4pSOipqCAi\nEgYsy+ruX9UTochR3dTB4q2VANyig5uIRJnCrGTOGZEDOMOEJTK8saWSQ61dDMhI4oLReabjSAxQ\nUcHPsqz7Lcua18vPkeX/PPdblnWvZVkPWZZ1V7Ayikh0u25aIS4LVpccYl9ti+k4chIWrinF47OZ\nNiSLsQMyTMcREQm6G/wF72fXlmLbtuE0cjICN+humjGIOLfe7knoxfx3mWVZ0y3Lega4F8jqxefJ\nAtYAT9m2/V3bth+wbftuYKRlWQ8FKa6IRLEBmUmcNyoX0MDGSGDbdvdk7VtnDjGcRkQkNC6dOICU\nBDclta2s9a/OlfC1r7aF93fXYllw00zdoJO+EbNFBcuy7rIsazFwM7A4CJ/yGWChbdtrD/9F27a/\nC9zU21sQIhIbFviHYj27rhSfT0+EwtkHe2opqW0lLTGOK6doQKOIRKfUxJ4htAvXqOAd7p70byOa\nXZTHoH4phtNIrIjZooJt2w/btj3f/6b/o958LsuyRgDzgGPdSHgauL83X0NEYsPF4weQlhjHgbo2\nVpfUmY4jx/GEf7L21VMHkpIQZziNiEjo3DC9EICXN5bT3uU1nEaOpcvr45mPNKBR+l7MFhWCbAGA\nbdt7jvH7u4Hp/hYJEZFjSk5wc/mkAYBaIMJZXUsnb2yuAOBTZ6r1QUSi29kjcijMSqap3cOSbZWm\n48gxLN1WSU1zB7lpicwd1990HIkhKioEx3yg/ji/Hyg2zOjNF2lsbDypj46Ojt58GRExLDAU65VN\nB2nr1BOhcPTs2lI6vT4mFmYwsTDTdBwRkZByuSyum+bcVli0RhuKwlXgBt2NMwYRrwGN0of03RYc\n2cDx7ikHCg4jevNFBg4cSGZm5gk/fv7zn/fmy4iIYTOHZTM4O5nmDg9vbq0wHUeOYNt2d8/qLRrQ\nKCIx4np/C8Ty4hqqmtoNp5EjlR5qZXlxNQC3aECj9DE1gQbHidoaAgWHXrU/lJeXk5qaesI/l5iY\n2JsvIyKGOU+EBvHbpcUsXFPKNVMLTUeSw6zZd4hdVc0kx7u5ZupA03FERPrEiLw0pg3JYt3+el5Y\nV86ds3v1rEyC7OmPSrFtOHdkDkNzTvx+QSSYdFMhOLI5fvtDQE5vvkhGRsZJfaioIBL5AkOx3ttV\nQ0WDngiFk3/5939fNaWA9KR4w2lERPpOoD1v0Vq1QIQTj9fH04EbdJrzIwaoqBAcGsAoIkE1NCeV\nmcP64bPh+fUa2BguGtq6eHXTQUAHNxGJPVdNHkhCnIvtFU1sKW8wHUf8lu2spqKxnX4p8VwyQQMa\npe+FffuDf2PCCJzbAKejzrbttUGMdDT1nFxhoTbEOUQkitwwfRCrSw6xaE0pd88egWVZpiPFvBfW\nl9He5WNM/3SmDVY9WURiS2ZKPPPH9eeVTQdZtKaMCQM1qDYcBAY03jB9EIlxbsNpJBaFfVEBuAu4\nu5efY2QwghzHiZbJBwoiJ9MiISICwOWTC7jvxS0UVzWzqayByYP0JtYk27b510qn9eGWMweryCMi\nMen66YW8sukgL6wv4/uXj9WWAcMqGtp5e0cV4Lw2iZgQ9kUF27YfAB4wneME1gILjvP7gXcCe47z\nZ0REPiYjKZ6LJwzgpQ3lPLu2TEUFwzaUNrC9oonEOFf3ajURkVgze3QeuWkJ1DR3snxnNXPH6bq9\nSc98dACvz2bmsH6Myk83HUdilEqLwbH4BL8/AsC27SV9kEVEokhgYOML68vo9PgMp4ltT/oHNF4+\nqYCslATDaUREzIh3u7q3Emlgo1k+n81TH2nFsZinokJwLAGwLGv6MX5/ZuDPiIicillFeeSnnjUR\n+QAAIABJREFUJ3Kotav7eqP0veYODy9uKAe0/1tEJLAFYsnWKupbOw2niV3v7qqh9FAbGUlxXDG5\nwHQciWEqKpwCy7KyLMu637KseYf/um3be3CKBsea/bAAuD/U+UQk+rhdVvdV+0Vr9ETIlJc2lNPa\n6WVEXipnDj/ducEiItFh/MAMxhVk0On18dLGg6bjxKwnVzs36K6bVkhSvAY0ijkqKjiyj/jnsdwF\n3MvR2x1uBOYdeVvBsqxngIfV+iAip+t6/xOht3dUUdeiJ0ImPOFvfbh15hANaBQRoac971m1QBhR\n3dTBm1sqAa04FvNitqhgWdYCy7IWW5a1m54iwUOWZe32//rRBi8uwdng8PCRv2Hbdj1wBnC3/zbD\nvZZlPQQstm27t9srRCSGjRmQzsTCDLq8Ni/5r+BL39lS3sDG0gbi3RbXT9eARhERgGumFuJ2Wazb\nX8/u6mbTcWLOorWleHw2UwZnMa4gw3QciXFhv/0hVGzbXggsPMV/Zy3Q7zi/X0/v11+KiHzCDdMH\nsblsK4vWlvLZc4eZjhNTnvTv/754wgBy0hINpxERCQ956YlcMDqPt7ZX8ezaUr5zyVjTkWKGbds8\ntdp5bbpVc34kDMTsTQURkUhy9ZSBxLksNpY2UFzZZDpOzGjr9PL8ujLAaX0QEZEegYGNz60tw+ez\nDaeJHR/uqWNvTQupCW6umjLQdBwRFRVERCJBTloic8bkA7BobZnhNLHj5Y3lNHV4GJKdwrkjc0zH\nEREJK3PH5ZORFEd5Qzsf7qk1HSdmBOb8XD21kNTEmL14LmFERQURkQix4Aynn/+5daV49USoTzzp\nv15688zBuFwa0CgicrikeDdX+p+UL9TAxj5xqKWT1zdXAHDrmWp9kPCgooKISIS4cGw+WSnxVDZ2\n8N6uGtNxot7OyibW7DuE22Vx4xmDTMcREQlLgRaI1zdX0NLhMZwm+j27roxOr4/xBRlMKsw0HUcE\nUFFBRCRiJMa5udr/REgrvEIvMKBx7th88jOSDKcREQlP04dkMTw3ldZOb/cTdAkN27Z5MrDi+Cyt\nOJbwoaKCiEgEuT7wRGhLBU3tXYbTRK/2Li/PrnMKN7eepQGNIiLHYlkW109z2vMWqeAdUmv3H6K4\nqpnkeDfXTNWARgkfKiqIiESQKYMyGZmXSnuXj9c26YlQqLyxpYL61i4Ks5KZXZRnOo6ISFi7brpT\nVPhgTy1l9W2G00Svf610btBdMbmAjKR4w2lEeqioICISQSzL4gZ/f7+GYoVOYLL2jTMG4daARhGR\n4xrUL4VzRuRg2/CcXptCoqGti1c2lQMa0CjhR0UFEZEIc920QiwLVu119lRLcO2taeHDPXW4LLhp\nhg5uIiIno7vgvUYbikLhxfVltHf5KMpPY/qQfqbjiHyMigoiIhGmIDOZC8fkA/C7t4oNp4k+T652\nbilcMDqPgVnJhtOIiESGyyYOIDM5npLaVl7aUG46TlSxbZt/+YcH33qmBjRK+FFRQUQkAn1jXhEA\nz68rY1dVs+E00aPT42PhR/4BjWdqQKOIyMlKTYzjrtkjAPj1kp14vD7DiaLHxtIGth1sJCHOxfX+\n+RUi4URFBRGRCDR5UBYXj++Pz3YObxIcS7ZVUtvSSX56IheNzTcdR0Qkonzu3GHkpCZQUtvKs2vL\nTMeJGoEbdJdNHEBWSoLhNCKfpKKCiEiE+ub80QC8vPEg2w42Gk4THQ4f0Bjn1kukiMipSE2M48tz\nRgLwm6XFdHi8hhNFvpYODy+ud9pJbpmpG3QSnnRiEhGJUOMKMrhycgEAv1qs2wq9daCulXd31QBw\n8wwd3ERETsdtZw8lPz2Rsvo2nl59wHSciPfShnJaOr0Mz03l7BHZpuOIHJWKCiIiEewb80bjsmDx\n1ko2ltabjhPRnlp9ANuGWUW5DMlJMR1HRCQiJcW7+dpFowB48O1dtHfptkJvBG7Q3TJzsAY0SthS\nUUFEJIKNyk/j2mnO0Kb/fVO3FU6Xx+vjmTXOEzVdLxUR6Z2bZg6mMCuZysYOHvtwn+k4EWtreSMb\nShuId1vdKztFwpGKCiIiEe7rc4uIc1ks21nNRyV1puNEpFc2HaSysYOc1ATmj+9vOo6ISERLjHPz\nb3Od2wp/fGc3LR0ew4ki0yPv7gVg/vj+5KYlGk4jcmwqKoiIRLihOancOGMwoNsKp6Ot08svXtsO\nwOfPG0ZCnF4aRUR66/rpgxiWk0JtSyd//6DEdJyIs+FAPYvWOiuO75w1wnAakePTyUlEJAp87aJR\nJLhdfLCnlvf9wwbl5Pxp2W4ONrRTmJXMF3VwExEJini3i6/PKwLgoWV7aGzvMpwocti2zX+9tAWA\n66YVMm1IP8OJRI5PRQURkSgwMCuZT53lzAL438U7sW3bcKLIUFbfxp+W7Qbgh1eMIynebTiRiEj0\nuHpKIaPy02ho6+Kv/qv8cmIvbihn7f56kuPdfPfSsabjiJyQigoiIlHiK3NGkhjnYs2+Q7yzs9p0\nnIjwi9e20+HxcdbwbC6bOMB0HBGRqOJ2WXxz3mgAHlmxl0MtnYYThb/WTk93S949F45kQGaS4UQi\nJ6aigohIlMjPSOKz5w4D4Fdv6rbCiawuqeOlDeVYFvzoqvFa1SUiEgKXTRzAuIIMmjo8PLxij+k4\nYe9Py/aoJU8ijooKIiJR5O7ZI0hNcLOprIE3t1aajhO2fL6eftVbZg5hwsBMw4lERKKTy2Xx7fnO\nbYVH3yuhprnDcKLwVVbfxkNqyZMIpKKCiEgUyUlL5PPnDQec2wo+n24rHM3CNaVsLmskPTGOb188\n2nQcEZGoNndcPlMGZ9HW5eWP7+w2HSds/fzVbXR4fJypljyJMCoqiIhEmTtnjSA9KY4dlU28vOmg\n6Thhp6m9iwfecPpVvz6vSLu/RURCzLJ6biv888N9VDS0G04UflbtrePljQexLLhPLXkSYVRUEBGJ\nMpkp8dzl78P89ZKdeLw+w4nCy4Nv76KmuZMRuancfs4w03FERGLCrKJczhyWTafHx+/f3mU6Tljx\nqiVPIpyKCiIiUejz5w+nX0o8e6pbeH59uek4YaOkpqV7rdl/XDmOhDi9DIqI9AXLsviWv93sydX7\nKT3UajhR+Fi45gBbytWSJ5FLpykRkSiUlhjHly4YCcBvlu6kS7cVAPjpq9vo8tpcMDqPC8fkm44j\nIhJTzh6Rw/mjcuny2vxuqW4rgNOS98s3dgBqyZPIpaKCiEiUuv2cYeSmJXKgro1nPio1Hce4FcXV\nLN5aidtl8f+uHKd+VRERAwK3FRauLWVvTYvhNOY9+JZa8iTyqaggIhKlkhPc3HOhc1vhd28V097l\nNZzIHI/Xx3+/vBWA288Zyqj8dMOJRERi0/Qh/bhobD5en81vluw0HceovTUt/PU9teRJ5NN3rohI\nFLv1zCEUZCZxsKGdJ1ftNx3HmH+t2s/Oymb6pcTzjbnqVxURMelb/k0QL2wop7iyyXAac376itOS\nN1steRLhVFQQEYliSfFuvnrRKAAefHs3bZ2xd1uhvrWTXy12noZ96+IxZKbEG04kIhLbJhZmcumE\nAdg2/F+M3lZYUVzNkm1OS96P1JInEU5FBRGRKHfjGYMZnJ1MTXMH//igxHScPvfrJcXUt3YxdkA6\nt84cbDqOiIgA35w/GsuCVzdVsKW8wXScPuXx+vjxS2rJk+ihooKISJRLiHPxdf+V/z8t201zh8dw\nor6zs7KJf364D4AfXTmeOLde9kREwsGYAelcPWUgAP+3OLZuKzy+cj/FVWrJk+ih05WISAy4dupA\nRuSmcqi1i7+9u9d0nD5h2zb//fJWvD6bSyb059xRuaYjiYjIYb4+twiXBUu2VbFu/yHTcfrEoRa1\n5En0UVFBRCQGxLldfMM/GOvhFXtoaO0ynCj0lm6rYkVxDQluFz+8fLzpOCIicoQReWncMH0QQPcb\n7Wj36yU7aWjrYkx/teRJ9FBRQUQkRlw5qYAx/dNpavfwl3f3mI4TUh0eLz95xelXvWPWcIbkpBhO\nJCIiR/Nvc4uIc1msKK5h5Z5a03FCamdlE4+tdDYx/egqteRJ9NB3sohIjHC5LL7pv63w13f3UtfS\naThR6Pz9/RJKalvJS0/kngtHmY4jIiLHMDg7hZv9T+z/d/FObNs2nCg0jmzJO08teRJFVFQQEYkh\nl0zoz8TCDFo6vTy0bLfpOCFR3dTBb5fuAuDeS8aQlhhnOJGIiBzPVy8aRUKci1V763hvV3TeVlii\nljyJYioqiIjEEMuy+Pb8MQD8/YMSKhvbzQYKgf95YwfNHR4mD8rs7tUVEZHwVZCZzKfPGgLA/7y5\nA58vum4rqCVPop2KCiIiMWbOmDymD8mivcvH155YR6fHZzpS0Gwua+DpNQcAuO+q8bhcluFEIiJy\nMr4yZxTJ8W7WH6jnN0uLTccJqkffK2GfWvIkiqmoICISYyzL4oEFk0lLjGPV3jr+66UtpiMFhW3b\n/NdLW7BtuGbqQM4Ymm06koiInKS89ER+fM0EAH6ztJjXNh00nCg4qps6+N1basmT6KaigohIDBqV\nn85vbpmKZcHjK/fz2If7TEfqtVc2HWR1ySGS4l1899KxpuOIiMgpunHGYL5w3nAAvvX0BrYdbDSc\nqPfUkiexQEUFEZEYNXdcf/79Yme+wn++uIUPI3iVV3uXl5+/uh2AL18wioFZyYYTiYjI6fjB5WOZ\nVZRLW5eXO//xUURvKlJLnsQKFRVERGLYV+aM5KopA/H4bL7y+FoO1LWajnRaHl6+h7L6Ngqzkrlr\n9gjTcURE5DTFuV387tZpDM1JofRQG195fA1d3sib/aOWPIklKiqIiMQwy7J44IbJTCzMoK6lkzv/\n8RGtnR7TsU5JeX0bf3jH6Vf93mVjSU5wG04kIiK9kZWSwF9un0FaYhwf7qnjxy9tNR3plL28US15\nEjtUVBARiXHJCW4e/swMctMS2F7RxL8/swHbjox1Xj6fzU9f2UZ7l4+Zw/px5eQC05FERCQIivqn\n8+ubndk///xwH/9aud90pJPW2N7Fz1/dBqglT2KDigoiIsLArGT+dNsZxLstXt1U0T2pOpy1dXr5\n2hPreGXTQSwL7rtqApalflURkWgxb3zP7J8fvbCZlREw+6ekpoXrfv8e5Q3tDMxMUkuexAQVFURE\nBIAZw7L5ybUTAfjV4p28vrnCcKJjq2ho56aHPuCVTQeJdwdaODJNxxIRkSD7ypyRXDm5AI/P5suP\nr6X0UPjO/nl/dw3X/uE9dle3MCAjiT9/doZa8iQmqKggIiLdbp45hM+dOwyAbz29nu0V4bfOa8OB\neq5+8F02lTWQnZrA4188mxtnDDYdS0REQsCyLH65YAoTBgZm/6wJy9k//1q5n9sfWUV9axdTBmfx\n4lfPY8JAFbslNqioICIiH/PDK8Zx7sgcWjvDb53XSxvKuemhD6hq6mB0/zReuOc8zhyuidoiItEs\nOcHNw7c7s3+2HWzkO89sDJvZPx6vj/98cQs/eG4THp/N1VMG8tRdZ5OfkWQ6mkifUVFBREQ+Jt7t\n4vefms6Q7BQO1LVxz+Nrja/z8vlsfrV4J197Yh0dHh8Xjc1n0ZfPZXB2itFcIiLSNwqzkvmjf/bP\nK5sO8mAYzP5paOviC3//iEffLwHg3y8ezW9umUpSvFoeJLaoqCAiIp/QLzWBP98+g9QENx/sqeUn\nL5tb59XW6eWrT6zlt0uLAbhr9gj+fPsM0pPijWUSEZG+N3NYNv99jTP7538X7+TNLeZm/5TUtHD9\nH95j+c5qkuPd/PHT0/nqRUUaGCwxSUUFERE5qjED0vm/m6cC8PcP9vHkqr5f53WwoY0bH3qfVzdV\nEO+2+OWCyfzg8nG4XTq0iYjEolvOHMJnzxkKwDefWs+OiqY+z/D+7hqu+b0zkLEgM4lnvnQOl03S\nSmOJXSoqiIjIMV08YQDfnj8agP94fjN/f7+kz/pY1x+o55oH32NzWSPZqQn8604NZBQREfiPK8dz\nzogcWjq93P7XlXxUUtdnX/vxlfu4/ZFVNLR1MXVwFi/cc562D0nMs8JlyIkcnWVZqUAzQHNzM6mp\nqYYTiUissW2bbz+9gWfXlQFw+aQB/OKGyWSEsP3gxQ3lfOeZDXR4fIzpn87/b+/+Y+Q47zqOf745\n/4h/xF6f1bS1FNKuJZIK2iZnR6pQUwE9K5VAggpfoiIIAsKdgP6DoGdZgGKhinCWEL/EH+fSSgVS\nKbFFoYhfuqv4o4GAGl9a2hAV4ksbqFsSxz6nOTs+2/flj3nW2ax3ZndnZ+ZmZ94vabV3uzPPPfd9\n5tmZ+T4zz/7Zzx1k/gQAwA0XVtc0Nf+0Xnj5dY3dYvrEA3dp+v6mbsnpSrZr19f1yb97/sb8CT9x\nzz7N/dT7mD8BlbW6uqqdO3e2ft3p7qtxy5JUKDmSCgDKwN31mX/5ph77++d1bd11597t+tOfnsh8\ndGZ93fWHi/+lPw4TcH347tv1Rx+7Vzu3bsr07wAARt/rV67pNz//Nf3NV85Kkn7krrfp9x+8R+M7\ntmT6dy5evqqPf25JX/rvc5KkTzxwl37lh/czfwIqjaRChZBUAFAmz750QR//3LP69splbRm7Rb/9\n4+/Rz3zgzkwOrC6tXdOvP/lV/cPXo4m3Zj7U1OxH7mb+BABALHfXE1/+Hz36hed05dq63rn7Vv3J\nx+7VwXdl83XDL55b1S9+9stafmVV2zaP6Q8eer8+8oPMn4DqI6lQISQVAJTNyqU1/cbJ/9Di8/8n\nSbr3+xr6pfubeuAH3pE6AfCdi5f1yGef0XNnX9PmMdPvfvS9zJ8AAOjb8995Tb/6+JKWz63qFpN+\n7H379MgH363339FIXea/vnBOv/z4ki5evqp37r5Vn3r4IPMnoDZIKlQISQUAZeTu+vRTL+r4P35D\na9fXJUl3jG/Tz//Qu/XgfXck3q7g7lq7vq7La9d1ae26ll9Z1a89+RW98r0r2rtji+Z/9kBmI0wA\ngPp4/co1/dbnv6a/DrdDSNJ979qjR+5vavI9b09MfLu73ri6rktr13Rp7br++Rsv63f+9j91bd11\nzx0NnXj4gG6/7dYi/g2gFEgqVAhJBQBl9vL33tBfPP0t/eW/fUsXLl2VJN22dZM+sH+vrlxb1+Vw\ncBY9op8vr13XtfWb9z13v+M2fephJmQEAAzn69++qM889aK+8NWzN/Y3d+7dru9/+20hod2+b7oe\n7auuXle306KfvGeffo8JGVFDJBUqhKQCgFFwee26/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "element_LGL_flat = af.flat(params.element_LGL)\n", + "E_z_init_flat = af.flat(E_z_init)\n", + "B_y_init_flat = af.flat(B_y_init)\n", + "\n", + "plt.plot(element_LGL_flat, E_z_init_flat, label = r'$E_z$')\n", + "plt.plot(element_LGL_flat, B_y_init_flat, label = r'$B_y$')\n", + "\n", + "plt.title(r'Plot of $E_z(t = 0)$ and $B_y(t = 0)$')\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "\n", + "plt.legend(prop={'size': 14})\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# 2. Modify the volume term to take flux as an argument.\n", + "\n", + "def volume_integral_flux(u_n, flux_n):\n", + " '''\n", + "\n", + " Calculates the volume integral of flux in the wave equation.\n", + "\n", + " :math:`\\\\int_{-1}^1 f(u) \\\\frac{d L_p}{d\\\\xi} d\\\\xi`\n", + "\n", + " This will give N values of flux integral as p varies from 0 to N - 1.\n", + " \n", + " This integral is carried out using the analytical form of the integrand\n", + " obtained as a linear combination of Lagrange basis polynomials.\n", + "\n", + " This integrand is the used in the integrate() function.\n", + "\n", + " Calculation of volume integral flux using N_LGL Lobatto quadrature points\n", + " can be vectorized and is much faster.\n", + " \n", + " Parameters\n", + " ----------\n", + "\n", + " u : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " Amplitude of the wave at the mapped LGL nodes of each element.\n", + "\n", + " flux_n : arrayfire:Array [N_LGL N_Elements 1 1]\n", + " Flux of the wave at the mapped LGL nodes of each element.\n", + "\n", + " Returns\n", + " -------\n", + "\n", + " flux_integral : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " Value of the volume integral flux. It contains the integral\n", + " of all N_LGL * N_Element integrands.\n", + "\n", + " '''\n", + " # The coefficients of dLp / d\\xi\n", + " diff_lag_coeff = params.dl_dxi_coeffs\n", + "\n", + " lobatto_nodes = params.lobatto_quadrature_nodes\n", + " Lobatto_weights = params.lobatto_weights_quadrature\n", + "\n", + " nodes_tile = af.transpose(af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1]))\n", + " power = af.flip(af.range(diff_lag_coeff.shape[1]))\n", + " power_tile = af.tile(power, 1, params.N_quad)\n", + " nodes_power = nodes_tile ** power_tile\n", + " weights_tile = af.transpose(af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1]))\n", + " nodes_weight = nodes_power * weights_tile\n", + "\n", + " dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight)\n", + "\n", + "\n", + " # The first option to calculate the volume integral term, directly uses\n", + " # the Lobatto quadrature instead of using the integrate() function by\n", + " # passing the coefficients of the Lagrange interpolated polynomial.\n", + " if(params.volume_integral_scheme == 'lobatto_quadrature' \\\n", + " and params.N_quad == params.N_LGL):\n", + "\n", + " # Flux using u_n, reordered to 1 X N_LGL X N_Elements array.\n", + " F_u_n = af.reorder(flux_n, 2, 0, 1)\n", + "\n", + " # Multiplying with dLp / d\\xi\n", + " integral_expansion = af.broadcast(utils.multiply,\n", + " dLp_dxi, F_u_n)\n", + "\n", + " # Using the quadrature rule.\n", + " flux_integral = af.sum(integral_expansion, 1)\n", + " flux_integral = af.reorder(flux_integral, 0, 2, 1)\n", + "\n", + " # Using the integrate() function to calculate the volume integral term\n", + " # by passing the Lagrange interpolated polynomial.\n", + " else:\n", + " #print('option3')\n", + " analytical_flux_coeffs = lagrange.lagrange_interpolation_u(flux_n)\n", + "\n", + " analytical_flux_coeffs = af.reorder(analytical_flux_coeffs, 1, 0, 2)\n", + "\n", + " dl_dxi_coefficients = af.reorder(params.dl_dxi_coeffs, 1, 0)\n", + "\n", + " # The product of polynomials is calculated using af.convolve1\n", + " volume_int_coeffs = af.convolve1(dl_dxi_coefficients,\n", + " analytical_flux_coeffs,\n", + " conv_mode=af.CONV_MODE.EXPAND)\n", + " volume_int_coeffs = af.reorder(volume_int_coeffs, 1, 2, 0)\n", + " volume_int_coeffs = af.moddims(volume_int_coeffs,\n", + " params.N_LGL * params.N_Elements,\n", + " 2 * params.N_LGL - 2)\n", + "\n", + " flux_integral = lagrange.integrate(volume_int_coeffs)\n", + " flux_integral = af.moddims(flux_integral, params.N_LGL, params.N_Elements)\n", + "\n", + "\n", + " return flux_integral\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/read_and_plot_mesh/read_and_plot_mesh.ipynb b/examples/read_and_plot_mesh/read_and_plot_mesh.ipynb index 6b808f5..85e8dbb 100644 --- a/examples/read_and_plot_mesh/read_and_plot_mesh.ipynb +++ b/examples/read_and_plot_mesh/read_and_plot_mesh.ipynb @@ -127,6 +127,18 @@ "display_name": "Python 3", "language": "python", "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" } }, "nbformat": 4, diff --git a/main.py b/main.py index ec9af31..2d24135 100644 --- a/main.py +++ b/main.py @@ -1,9 +1,13 @@ #! /usr/bin/env python3 +import arrayfire as af +af.set_backend('opencl') +af.set_device(0) +af.info() + from dg_maxwell import wave_equation from dg_maxwell import lagrange - if __name__ == '__main__': u_diff = wave_equation.time_evolution() print(lagrange.L1_norm(u_diff)) From 202a97a5aedcdca2881969a4e1fd363141daebbf Mon Sep 17 00:00:00 2001 From: AAT Date: Sat, 9 Dec 2017 07:05:49 +0530 Subject: [PATCH 02/13] Code refactored to handle general flux. RK4 currently giving flux_x(u) for flux to b_vector. This has to be changed for different cases. --- dg_maxwell/__init__.py | 2 +- dg_maxwell/isoparam.py | 2 +- dg_maxwell/lagrange.py | 2 +- dg_maxwell/msh_parser.py | 2 +- dg_maxwell/params.py | 4 +- dg_maxwell/tests/convergence_tests.py | 2 +- dg_maxwell/tests/isoparam/test_isoparam.py | 2 +- .../tests/msh_parser/test_msh_parser.py | 2 +- dg_maxwell/tests/test_waveEqn.py | 81 ++++++- dg_maxwell/utils.py | 2 +- dg_maxwell/wave_equation.py | 192 ++++++++++++++- .../maxwell's_equations_1d.ipynb | 220 +++++++++++++++++- main.py | 2 +- 13 files changed, 490 insertions(+), 25 deletions(-) diff --git a/dg_maxwell/__init__.py b/dg_maxwell/__init__.py index 73cf99f..d871a9c 100644 --- a/dg_maxwell/__init__.py +++ b/dg_maxwell/__init__.py @@ -3,6 +3,6 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) from dg_maxwell import params diff --git a/dg_maxwell/isoparam.py b/dg_maxwell/isoparam.py index 5579701..3d3c0ff 100644 --- a/dg_maxwell/isoparam.py +++ b/dg_maxwell/isoparam.py @@ -3,7 +3,7 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) from dg_maxwell import utils diff --git a/dg_maxwell/lagrange.py b/dg_maxwell/lagrange.py index 2029de2..b7315ac 100644 --- a/dg_maxwell/lagrange.py +++ b/dg_maxwell/lagrange.py @@ -5,7 +5,7 @@ from scipy import special as sp import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) from dg_maxwell import utils from dg_maxwell import params diff --git a/dg_maxwell/msh_parser.py b/dg_maxwell/msh_parser.py index b91fb3f..d10a80c 100644 --- a/dg_maxwell/msh_parser.py +++ b/dg_maxwell/msh_parser.py @@ -6,7 +6,7 @@ import gmshtranslator.gmshtranslator as gmsh import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) from dg_maxwell import msh_parser from dg_maxwell import isoparam diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index 731e4d6..3620f34 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -4,7 +4,7 @@ import numpy as np import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) from dg_maxwell import lagrange from dg_maxwell import utils @@ -32,7 +32,7 @@ N_quad = 8 # Wave speed. -c = 1. +c = 0.5 # The total time for which the wave is to be evolved by the simulation. total_time = 2.01 diff --git a/dg_maxwell/tests/convergence_tests.py b/dg_maxwell/tests/convergence_tests.py index 04b5953..45887e8 100644 --- a/dg_maxwell/tests/convergence_tests.py +++ b/dg_maxwell/tests/convergence_tests.py @@ -3,7 +3,7 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) def L1_norm(u): ''' diff --git a/dg_maxwell/tests/isoparam/test_isoparam.py b/dg_maxwell/tests/isoparam/test_isoparam.py index cfa2bee..e750e68 100644 --- a/dg_maxwell/tests/isoparam/test_isoparam.py +++ b/dg_maxwell/tests/isoparam/test_isoparam.py @@ -7,7 +7,7 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) import numpy as np diff --git a/dg_maxwell/tests/msh_parser/test_msh_parser.py b/dg_maxwell/tests/msh_parser/test_msh_parser.py index 11ab2e4..a563f33 100644 --- a/dg_maxwell/tests/msh_parser/test_msh_parser.py +++ b/dg_maxwell/tests/msh_parser/test_msh_parser.py @@ -7,7 +7,7 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) import numpy as np diff --git a/dg_maxwell/tests/test_waveEqn.py b/dg_maxwell/tests/test_waveEqn.py index d0c2c76..47e7d4c 100644 --- a/dg_maxwell/tests/test_waveEqn.py +++ b/dg_maxwell/tests/test_waveEqn.py @@ -8,7 +8,7 @@ import numpy as np import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) from dg_maxwell import params from dg_maxwell import lagrange @@ -447,6 +447,23 @@ def test_lax_friedrichs_flux(): assert af.max(af.abs(analytical_lax_friedrichs_flux - f_i)) < threshold + +def test_lax_friedrichs_flux_u_n_flux_n(): + ''' + A test function to test the lax_friedrichs_flux function in wave_equation + module. + ''' + threshold = 1e-14 + + params.c = 1 + + f_i = wave_equation.lax_friedrichs_flux_u_n_flux_n(params.u[:, :, 0], + wave_equation.flux_x( + params.u[:, :, 0])) + analytical_lax_friedrichs_flux = params.u[-1, :, 0] + assert af.max(af.abs(analytical_lax_friedrichs_flux - f_i)) < threshold + + def test_surface_term(): ''' A test function to test the surface_term function in the wave_equation @@ -475,6 +492,39 @@ def test_surface_term(): return analytical_surface_term + +def test_surface_term_u_n_flux_n(): + ''' + A test function to test the surface_term function in the wave_equation + module using analytical Lax-Friedrichs flux. + ''' + threshold = 1e-13 + params.c = 1 + + change_parameters(8, 10, 8, 'gaussian') + + analytical_f_i = (params.u[-1, :, 0]) + analytical_f_i_minus1 = (af.shift(params.u[-1, :, 0], 0, 1)) + + L_p_1 = af.constant(0, params.N_LGL, dtype = af.Dtype.f64) + L_p_1[params.N_LGL - 1] = 1 + + L_p_minus1 = af.constant(0, params.N_LGL, dtype = af.Dtype.f64) + L_p_minus1[0] = 1 + + analytical_surface_term = af.blas.matmul(L_p_1, analytical_f_i)\ + - af.blas.matmul(L_p_minus1, analytical_f_i_minus1) + + numerical_surface_term = wave_equation.surface_term_u_n_flux_n( + params.u[:, :, 0], + wave_equation.lax_friedrichs_flux(params.u[:, :, 0])) + + assert af.max(af.abs(analytical_surface_term - numerical_surface_term)) \ + < threshold + return analytical_surface_term + + + def test_b_vector(): ''' A test function to check the b vector obtained analytically and compare it @@ -495,6 +545,35 @@ def test_b_vector(): assert (b_vector_analytical - b_vector_array) < threshold + +def test_b_vector_u_n_flux_n(): + ''' + A test function to check the b vector obtained analytically and compare it + with the one returned by b_vector function in wave_equation module. + ''' + threshold = 1e-13 + params.c = 1 + + change_parameters(8, 10, 8, 'gaussian') + + u_n_A_matrix = af.blas.matmul(wave_equation.A_matrix(), + params.u[:, :, 0]) + volume_integral_flux = wave_equation.volume_integral_flux_u_n_flux_n( + params.u[:, :, 0], wave_equation.flux_x(params.u[:, :, 0])) + + surface_term = test_surface_term_u_n_flux_n() + + b_vector_analytical = u_n_A_matrix \ + + (volume_integral_flux - surface_term) \ + * params.delta_t + + b_vector_array = wave_equation.b_vector_u_n_flux_n( + params.u[:, :, 0], wave_equation.flux_x(params.u[:, :, 0])) + + assert (b_vector_analytical - b_vector_array) < threshold + + + def test_integrate(): ''' Testing the integrate() function by passing coefficients diff --git a/dg_maxwell/utils.py b/dg_maxwell/utils.py index 45880c8..fca9125 100644 --- a/dg_maxwell/utils.py +++ b/dg_maxwell/utils.py @@ -5,7 +5,7 @@ import matplotlib.lines as lines import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) def add(a, b): ''' diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index d0cd674..9546982 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -5,7 +5,7 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) import numpy as np from matplotlib import pyplot as plt @@ -292,6 +292,8 @@ def volume_integral_flux(u_n): return flux_integral + + def volume_integral_flux_u_n_flux_n(u_n, flux_n): ''' @@ -385,6 +387,7 @@ def volume_integral_flux_u_n_flux_n(u_n, flux_n): return flux_integral + def lax_friedrichs_flux(u_n): ''' @@ -424,6 +427,56 @@ def lax_friedrichs_flux(u_n): return boundary_flux + + +def lax_friedrichs_flux_u_n_flux_n(u_n, flux_n): + ''' + + Calculates the lax-friedrichs_flux :math:`f_i` using. + + :math:`f_i = \\frac{F(u^{i + 1}_0) + F(u^i_{N_{LGL} - 1})}{2} - \\frac + {\Delta x}{2\Delta t} (u^{i + 1}_0 - u^i_{N_{LGL} - 1})` + + The algorithm used is explained in this `document`_ + + .. _document: `https://goo.gl/sNsXXK` + + + Parameters + ---------- + + u_n : arrayfire.Array [N_LGL N_Elements 1 1] + Amplitude of the wave at the mapped LGL nodes of each element. + + f_n : arrayfire:Array [N_LGL N_Elements 1 1] + Flux of the wave at the mapped LGL nodes of each element. + + Returns + ------- + + boundary_flux : arrayfire.Array [1 N_Elements 1 1] + Contains the value of the flux at the boundary elements. + Periodic boundary conditions are used. + + ''' + + u_iplus1_0 = af.shift(u_n[0, :], 0, -1) + flux_iplus1_0 = af.shift(u_n[0, :], 0, -1) + + u_i_N_LGL = u_n[-1, :] + flux_i_N_LGL = flux_n[-1, :] + + flux_iplus1_0 = flux_x(u_iplus1_0) + flux_i_N_LGL = flux_x(u_i_N_LGL) + + boundary_flux = (flux_iplus1_0 + flux_i_N_LGL) / 2 \ + - params.c_lax * (u_iplus1_0 - u_i_N_LGL) / 2 + + + return boundary_flux + + + def analytical_u_LGL(t_n): ''' @@ -448,6 +501,8 @@ def analytical_u_LGL(t_n): return u_t_n + + def surface_term(u_n): ''' @@ -486,6 +541,47 @@ def surface_term(u_n): return surface_term +def surface_term_u_n_flux_n(u_n, LF_flux_i): + ''' + + Calculates the surface term, + :math:`L_p(1) f_i - L_p(-1) f_{i - 1}` + using the lax_friedrichs_flux function and lagrange_basis_value + from params module. + + Parameters + ---------- + u_n : arrayfire.Array [N_LGL N_Elements 1 1] + Amplitude of the wave at the mapped LGL nodes of each element. + + flux_n : af.Array [N_LGL N_Elements 1 1] + Lax Friedrichs flux of the wave at the mapped LGL nodes of each element. + + Returns + ------- + surface_term : arrayfire.Array [N_LGL N_Elements 1 1] + The surface term represented in the form of an array, + :math:`L_p (1) f_i - L_p (-1) f_{i - 1}`, where p varies + from zero to :math:`N_{LGL}` and i from zero to + :math:`N_{Elements}`. p varies along the rows and i along + columns. + + **See:** `PDF`_ describing the algorithm to obtain the surface term. + + .. _PDF: https://goo.gl/Nhhgzx + + ''' + + L_p_minus1 = params.lagrange_basis_value[:, 0] + L_p_1 = params.lagrange_basis_value[:, -1] + LF_flus_iminus1 = af.shift(LF_flux_i, 0, 1) + surface_term = af.blas.matmul(L_p_1, LF_flux_i) \ + - af.blas.matmul(L_p_minus1, LF_flus_iminus1) + + return surface_term + + + def b_vector(u_n): ''' @@ -510,12 +606,52 @@ def b_vector(u_n): ''' volume_integral = volume_integral_flux(u_n) - #volume_integral = volume_integral_flux_u_n_flux_n(u_n, flux_x(u_n)) - Surface_term = surface_term(u_n) + Surface_term = surface_term(u_n) b_vector_array = (volume_integral - Surface_term) return b_vector_array + + +# 5. Modify the b vector to accept the flux as an argument + +def b_vector_u_n_flux_n(u_n, flux_n): + ''' + + Calculates the b vector for N_Elements number of elements. + + Parameters + ---------- + + u_n : arrayfire.Array [N_LGL N_Elements 1 1] + Amplitude of the wave at the mapped LGL nodes of each element. + + flux_n : af.Array [N_LGL N_Elements 1 1] + Flux of the wave at the mapped LGL nodes of each element. + + Returns + ------- + + b_vector_array : arrayfire.Array [N_LGL N_Elements 1 1] + Contains the b vector(of shape [N_LGL 1 1 1]) + for each element. + + **See:** `Report`_ for the b-vector can be found here + + .. _Report: https://goo.gl/sNsXXK + + ''' + volume_integral = volume_integral_flux_u_n_flux_n(u_n, flux_n) + Surface_term = surface_term_u_n_flux_n( + u_n, + lax_friedrichs_flux_u_n_flux_n(u_n, flux_n)) + + b_vector_array = (volume_integral - Surface_term) + + return b_vector_array + + + def RK4_timestepping(A_inverse, u, delta_t): ''' @@ -540,15 +676,58 @@ def RK4_timestepping(A_inverse, u, delta_t): ''' - k1 = af.matmul(A_inverse, b_vector(u )) + k1 = af.matmul(A_inverse, b_vector(u)) k2 = af.matmul(A_inverse, b_vector(u + k1 * delta_t / 2)) k3 = af.matmul(A_inverse, b_vector(u + k2 * delta_t / 2)) - k4 = af.matmul(A_inverse, b_vector(u + k3 * delta_t )) + k4 = af.matmul(A_inverse, b_vector(u + k3 * delta_t)) delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6 return delta_u + + +def RK4_timestepping_u_n_flux_n(A_inverse, u, flux, delta_t): + ''' + + Implementing the Runge-Kutta (RK4) method to evolve the wave. + + Parameters + ---------- + A_inverse : arrayfire.Array[N_LGL N_LGL 1 1] + The inverse of the A matrix which was calculated + using A_matrix() function. + + u : arrayfire.Array[N_LGL N_Elements 1 1] + u at the mapped LGL points + + flux : af.Array [N_LGL N_Elements 1 1] + Flux of the wave at the mapped LGL nodes of each element. + + delta_t : float64 + The time-step by which u is to be evolved. + + Returns + ------- + delta_u : arrayfire.Array [N_LGL N_Elements 1 1] + The change in u at the mapped LGL points. + + ''' + + k1 = af.matmul(A_inverse, b_vector_u_n_flux_n(u, flux_x(u))) + k2 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k1 * delta_t / 2, + flux_x(u + k1 * delta_t / 2))) + k3 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k2 * delta_t / 2, + flux_x(u + k2 * delta_t / 2))) + k4 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k3 * delta_t, + flux_x(u + k3 * delta_t))) + + delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6 + + return delta_u + + + def RK6_timestepping(A_inverse, u, delta_t): ''' @@ -607,6 +786,7 @@ def RK6_timestepping(A_inverse, u, delta_t): return delta_u + def time_evolution(): ''' @@ -662,7 +842,7 @@ def time_evolution(): # * delta_t # Implementing RK 4 scheme - u += RK4_timestepping(A_inverse, u, delta_t) + u += RK4_timestepping_u_n_flux_n(A_inverse, u, flux_x(u), delta_t) # Implementing RK 6 scheme #u += RK6_timestepping(A_inverse, u, delta_t) diff --git a/examples/maxwells_equations/maxwell's_equations_1d.ipynb b/examples/maxwells_equations/maxwell's_equations_1d.ipynb index f69c9f6..a041462 100644 --- a/examples/maxwells_equations/maxwell's_equations_1d.ipynb +++ b/examples/maxwells_equations/maxwell's_equations_1d.ipynb @@ -2,9 +2,20 @@ "cells": [ { "cell_type": "code", - "execution_count": 16, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1193: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n", + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1220: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n" + ] + } + ], "source": [ "import os\n", "import sys\n", @@ -19,6 +30,8 @@ "from dg_maxwell import wave_equation as w1d\n", "\n", "af.set_backend('opencl')\n", + "af.set_device(1)\n", + "af.info()\n", "\n", "plt.rcParams['figure.figsize'] = 12, 7.5\n", "plt.rcParams['lines.linewidth'] = 1.5\n", @@ -52,7 +65,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -73,14 +86,14 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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XtASAtyoBtAMo0r/SAZRJKTd5k1AgIiIiIiIiCjYRu1JBCFEMYDuAagAV0FYZ+EKJlNLq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ycc4O2fMqT6HYZkp+Dx2azaW2c2m4SHD34PG57ouVqalm860Wnz+uzug9u5OriJhK9zvgoTrgef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\n7auuXle306KfvGeffo8JGVFDJBUqhKQCgFFwee26/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v9VXVIRERRZyjR4+isLBw3Pt27twJq9WKmpqaAEc1PiYVKOQ8/doZtPUOYVFW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\nvEn+yxWw9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sdgWVZ3IWHxlmOsCxYJkXcDbXlzRuvBivTQKUVE5BScNyqP5AQX5Q3tbDnY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\nAEhk62ZXAAAAIE1mNh3+WJd0wd0nzawm6XjTYm+4+8n8awcAQ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -106,7 +119,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -205,6 +218,199 @@ " return flux_integral\n" ] }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# 3. Modify the Lax Friedrichs flux to accept the f_n and f_n+1 as argument\n", + "\n", + "def lax_friedrichs_flux_u_n_flux_n(u_n, flux_n):\n", + " '''\n", + "\n", + " Calculates the lax-friedrichs_flux :math:`f_i` using.\n", + "\n", + " :math:`f_i = \\\\frac{F(u^{i + 1}_0) + F(u^i_{N_{LGL} - 1})}{2} - \\\\frac\n", + " {\\Delta x}{2\\Delta t} (u^{i + 1}_0 - u^i_{N_{LGL} - 1})`\n", + "\n", + " The algorithm used is explained in this `document`_\n", + "\n", + " .. _document: `https://goo.gl/sNsXXK`\n", + "\n", + "\n", + " Parameters\n", + " ----------\n", + "\n", + " u_n : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " Amplitude of the wave at the mapped LGL nodes of each element.\n", + "\n", + " flux_n : arrayfire:Array [N_LGL N_Elements 1 1]\n", + " Flux of the wave at the mapped LGL nodes of each element.\n", + "\n", + " Returns\n", + " -------\n", + "\n", + " boundary_flux : arrayfire.Array [1 N_Elements 1 1]\n", + " Contains the value of the flux at the boundary elements.\n", + " Periodic boundary conditions are used.\n", + "\n", + " '''\n", + " \n", + " u_iplus1_0 = af.shift(u_n[0, :], 0, -1)\n", + " flux_iplus1_0 = af.shift(u_n[0, :], 0, -1)\n", + "\n", + " u_i_N_LGL = u_n[-1, :]\n", + " flux_i_N_LGL = flux_n[-1, :]\n", + "\n", + " flux_iplus1_0 = flux_x(u_iplus1_0)\n", + " flux_i_N_LGL = flux_x(u_i_N_LGL)\n", + " \n", + " boundary_flux = (flux_iplus1_0 + flux_i_N_LGL) / 2 \\\n", + " - params.c_lax * (u_iplus1_0 - u_i_N_LGL) / 2\n", + " \n", + " \n", + " return boundary_flux \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 4. Modufy the surface term to work for flux as an argument.\n", + "\n", + "def surface_term_u_n_flux_n(u_n, flux_i):\n", + " '''\n", + "\n", + " Calculates the surface term,\n", + " :math:`L_p(1) f_i - L_p(-1) f_{i - 1}`\n", + " using the lax_friedrichs_flux function and lagrange_basis_value\n", + " from params module.\n", + " \n", + " Parameters\n", + " ----------\n", + " u_n : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " Amplitude of the wave at the mapped LGL nodes of each element.\n", + "\n", + " flux_n : af.Array [N_LGL N_Elements 1 1]\n", + " Flux of the wave at the mapped LGL nodes of each element.\n", + "\n", + " Returns\n", + " -------\n", + " surface_term : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " The surface term represented in the form of an array,\n", + " :math:`L_p (1) f_i - L_p (-1) f_{i - 1}`, where p varies\n", + " from zero to :math:`N_{LGL}` and i from zero to\n", + " :math:`N_{Elements}`. p varies along the rows and i along\n", + " columns.\n", + " \n", + " **See:** `PDF`_ describing the algorithm to obtain the surface term.\n", + " \n", + " .. _PDF: https://goo.gl/Nhhgzx\n", + "\n", + " '''\n", + "\n", + " L_p_minus1 = params.lagrange_basis_value[:, 0]\n", + " L_p_1 = params.lagrange_basis_value[:, -1]\n", + "# f_i = lax_friedrichs_flux(u_n)\n", + " f_iminus1 = af.shift(flux_i, 0, 1)\n", + " surface_term = af.blas.matmul(L_p_1, flux_i) \\\n", + " - af.blas.matmul(L_p_minus1, f_iminus1)\n", + " \n", + " return surface_term\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 5. Modify the b vector to accept the flux as an argument\n", + "\n", + "def b_vector_u_n_flux_n(u_n, flux_n):\n", + " '''\n", + "\n", + " Calculates the b vector for N_Elements number of elements.\n", + " \n", + " Parameters\n", + " ----------\n", + "\n", + " u_n : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " Amplitude of the wave at the mapped LGL nodes of each element.\n", + "\n", + " flux_n : af.Array [N_LGL N_Elements 1 1]\n", + " Flux of the wave at the mapped LGL nodes of each element.\n", + "\n", + " Returns\n", + " -------\n", + "\n", + " b_vector_array : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " Contains the b vector(of shape [N_LGL 1 1 1])\n", + " for each element.\n", + "\n", + " **See:** `Report`_ for the b-vector can be found here\n", + "\n", + " .. _Report: https://goo.gl/sNsXXK\n", + "\n", + " '''\n", + " volume_integral = volume_integral_flux_u_n_flux_n(u_n, flux_n)\n", + " Surface_term = surface_term_u_n_flux_n(\n", + " u_n,\n", + " lax_friedrichs_flux_u_n_flux_n(u_n, flux_n))\n", + " \n", + " b_vector_array = (volume_integral - Surface_term)\n", + " \n", + " return b_vector_array\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 6. Modify the RK4 time stepping function to take flux as an argument.\n", + "\n", + "def RK4_timestepping_u_n_flux_n(A_inverse, u, flux, delta_t):\n", + " '''\n", + "\n", + " Implementing the Runge-Kutta (RK4) method to evolve the wave.\n", + "\n", + " Parameters\n", + " ----------\n", + " A_inverse : arrayfire.Array[N_LGL N_LGL 1 1]\n", + " The inverse of the A matrix which was calculated\n", + " using A_matrix() function.\n", + "\n", + " u : arrayfire.Array[N_LGL N_Elements 1 1]\n", + " u at the mapped LGL points\n", + "\n", + " flux_n : arrayfire.Array[N_LGL N_Elements 1 1]\n", + " \n", + "\n", + " delta_t : float64\n", + " The time-step by which u is to be evolved.\n", + "\n", + " Returns\n", + " -------\n", + " delta_u : arrayfire.Array [N_LGL N_Elements 1 1]\n", + " The change in u at the mapped LGL points.\n", + "\n", + " '''\n", + "\n", + " k1 = af.matmul(A_inverse, b_vector_u_n_flux_n(u, flux))\n", + " k2 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k1 * delta_t / 2, flux))\n", + " k3 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k2 * delta_t / 2, flux))\n", + " k4 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k3 * delta_t, flux))\n", + "\n", + " delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6\n", + "\n", + " return delta_u\n" + ] + }, { "cell_type": "code", "execution_count": null, diff --git a/main.py b/main.py index 2d24135..3649599 100644 --- a/main.py +++ b/main.py @@ -2,7 +2,7 @@ import arrayfire as af af.set_backend('opencl') -af.set_device(0) +af.set_device(1) af.info() from dg_maxwell import wave_equation From 44f9523db0400126cf19c5d1cb94fd747982561b Mon Sep 17 00:00:00 2001 From: AAT Date: Sat, 9 Dec 2017 16:35:38 +0530 Subject: [PATCH 03/13] Volume integral term which accept multiple u's written. - Documentation written. - Unit tests passing. - Throughly tested for both options of volume integral calculation for different values of c in both directions. --- .gitignore | 1 + dg_maxwell/lagrange.py | 25 ++ dg_maxwell/tests/test_waveEqn.py | 55 +++ dg_maxwell/utils.py | 60 +++ dg_maxwell/wave_equation.py | 141 ++++++- ...s_1d.ipynb => maxwells_equations_1d.ipynb} | 0 .../maxwells_equations_vetorised_flux.ipynb | 372 ++++++++++++++++++ 7 files changed, 650 insertions(+), 4 deletions(-) rename examples/maxwells_equations/{maxwell's_equations_1d.ipynb => maxwells_equations_1d.ipynb} (100%) create mode 100644 examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb diff --git a/.gitignore b/.gitignore index 0edc383..728c59f 100644 --- a/.gitignore +++ b/.gitignore @@ -198,4 +198,5 @@ Thumbs.db !dg_maxwell/tests/mesh/* !dg_maxwell/tests/msh_parser/mesh/* !examples/maxwells_equations/* +!examples/lagrange_interpolation_general/* !docs/quazar_logo.png diff --git a/dg_maxwell/lagrange.py b/dg_maxwell/lagrange.py index b7315ac..5acf673 100644 --- a/dg_maxwell/lagrange.py +++ b/dg_maxwell/lagrange.py @@ -377,3 +377,28 @@ def L1_norm(u): L1_norm = af.sum(integrate(interpolated_coeffs)) return L1_norm + + +def lagrange_interpolation(fn_i): + ''' + Finds the general interpolation of a function. + + Parameters + ---------- + fn_i : af.Array [N N_LGL 1 1] + Value of :math:`N` functions at the LGL points. + + Returns + ------- + lagrange_interpolation : af.Array [N N_LGL 1 1] + :math:`N` interpolated polynomials for + :math:`N` functions. + ''' + + fn_i = af.transpose(af.reorder(fn_i, d0 = 2, d1 = 1, d2 = 0)) + lagrange_interpolation = af.broadcast(utils.multiply, + params.lagrange_coeffs, fn_i) + lagrange_interpolation = af.reorder(af.sum(lagrange_interpolation, dim = 0), + d0 = 2, d1 = 1, d2 = 0) + + return lagrange_interpolation diff --git a/dg_maxwell/tests/test_waveEqn.py b/dg_maxwell/tests/test_waveEqn.py index 47e7d4c..2532fdc 100644 --- a/dg_maxwell/tests/test_waveEqn.py +++ b/dg_maxwell/tests/test_waveEqn.py @@ -374,6 +374,61 @@ def test_volume_integral_flux(): numerical_flux = wave_equation.volume_integral_flux(params.u[:, :, 0]) assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) +def test_volume_integral_flux_multiple_u_n(): + ''' + A test function to check the volume_integral_flux function in wave_equation + module by analytically calculated Gauss-Lobatto quadrature. + + Reference + --------- + The link to the sage worksheet where the calculations were caried out is + given below. + `https://goo.gl/5Mub8M` + ''' + threshold = 4e-9 + params.c = 1 + change_parameters(8, 10, 11, 'gaussian') + + referenceFluxIntegral = af.transpose(af.interop.np_to_af_array(np.array + ([ + [-0.002016634876668093, -0.000588597708116113, -0.0013016773719126333,\ + -0.002368387579324652, -0.003620502047659841, -0.004320197094090966, + -0.003445512010153811, 0.0176615086879261],\ + + [-0.018969769374, -0.00431252844519,-0.00882630935977,-0.0144355176966,\ + -0.019612124119, -0.0209837936827, -0.0154359890788, 0.102576031756], \ + + [-0.108222418798, -0.0179274222595, -0.0337807018822, -0.0492589052599,\ + -0.0588472807471, -0.0557970236273, -0.0374764132459, 0.361310165819],\ + + [-0.374448714304, -0.0399576371245, -0.0683852285846, -0.0869229749357,\ + -0.0884322503841, -0.0714664112839, -0.0422339853622, 0.771847201979], \ + + [-0.785754362849, -0.0396035640187, -0.0579313769517, -0.0569022801117,\ + -0.0392041960688, -0.0172295769141, -0.00337464521455, 1.00000000213],\ + + [-1.00000000213, 0.00337464521455, 0.0172295769141, 0.0392041960688,\ + 0.0569022801117, 0.0579313769517, 0.0396035640187, 0.785754362849],\ + + [-0.771847201979, 0.0422339853622, 0.0714664112839, 0.0884322503841, \ + 0.0869229749357, 0.0683852285846, 0.0399576371245, 0.374448714304],\ + + [-0.361310165819, 0.0374764132459, 0.0557970236273, 0.0588472807471,\ + 0.0492589052599, 0.0337807018822, 0.0179274222595, 0.108222418798], \ + + [-0.102576031756, 0.0154359890788, 0.0209837936827, 0.019612124119, \ + 0.0144355176966, 0.00882630935977, 0.00431252844519, 0.018969769374],\ + + [-0.0176615086879, 0.00344551201015 ,0.00432019709409, 0.00362050204766,\ + 0.00236838757932, 0.00130167737191, 0.000588597708116, 0.00201663487667]\ + + ]))) + + numerical_flux = wave_equation.volume_integral_flux_multiple_u_n( + params.u[:, :, 0]) + assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) + + def test_volume_integral_flux_u_n_flux_n(): ''' diff --git a/dg_maxwell/utils.py b/dg_maxwell/utils.py index fca9125..42bee16 100644 --- a/dg_maxwell/utils.py +++ b/dg_maxwell/utils.py @@ -168,3 +168,63 @@ def plot_line(points, axes_handler, grid_width = 2., grid_color = 'blue'): axes_handler.add_line(lines.Line2D(line1_xs, line1_ys, linewidth=grid_width, color=grid_color)) return + + +def shape(array): + ''' + ''' + af_shape = array.shape + + shape = [1, 1, 1, 1] + + for dim in np.arange(array.numdims()): + shape[dim] = af_shape[dim] + + return shape + + + +def polyval_1d(polynomials, xi): + ''' + Finds the value of the polynomials at the given :math:`\\xi` coordinates. + Parameters + ---------- + polynomials : af.Array [number_of_polynomials N 1 1] + ``number_of_polynomials`` :math:`2D` polynomials of degree + :math:`N - 1` of the form + .. math:: P(x) = a_0x^0 + a_1x^1 + ... \\ + a_{N - 1}x^{N - 1} + a_Nx^N + xi : af.Array [N 1 1 1] + :math:`\\xi` coordinates at which the :math:`i^{th}` Lagrange + basis polynomial is to be evaluated. + Returns + ------- + af.Array [i.shape[0] xi.shape[0] 1 1] + Evaluated polynomials at given :math:`\\xi` coordinates + ''' + + N = int(polynomials.shape[1]) + xi_ = af.tile(af.transpose(xi), d0 = N) + power = af.tile(af.flip(af.range(N), dim = 0), + d0 = 1, d1 = xi.shape[0]) + + xi_power = xi_**power + + return af.matmul(polynomials, xi_power) + + + +def poly1d_product(poly_a, poly_b): + ''' + Finds the product of two polynomials using the arrayfire convolve1 + function. + Parameters + ---------- + poly_a : af.Array[N degree_a 1 1] + :math:`N` polynomials of degree :math:`degree` + poly_b : af.Array[N degree_b 1 1] + :math:`N` polynomials of degree :math:`degree_b` + ''' + return af.transpose(af.convolve1(af.transpose(poly_a), + af.transpose(poly_b), + conv_mode = af.CONV_MODE.EXPAND)) diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 9546982..9f144cc 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -201,6 +201,22 @@ def flux_x(u): return flux +def flux_maxwell(cons_var): + ''' + Fluxes for the :math:`(E_z, B_y)` mode in :math:`1D` Maxwell's equations. + + Parameters + ---------- + + cons_var : af.Array [N_Elements 2] + ''' + + E_z = cons_var[0] + B_y = cons_var[1] + + return (-B_y, E_z) + + def volume_integral_flux(u_n): ''' @@ -294,7 +310,7 @@ def volume_integral_flux(u_n): -def volume_integral_flux_u_n_flux_n(u_n, flux_n): +def volume_integral_flux_multiple_u_n(u_n): ''' Calculates the volume integral of flux in the wave equation. @@ -314,6 +330,124 @@ def volume_integral_flux_u_n_flux_n(u_n, flux_n): Parameters ---------- + u : arrayfire.Array [N_LGL N_Elements M 1] + Amplitude of the wave at the mapped LGL nodes of each element. This + function can computer flux for :math:`M` :math:`u` simultaneously. + + Returns + ------- + + flux_integral : arrayfire.Array [N_LGL N_Elements 1 1] + Value of the volume integral flux. It contains the integral + of all N_LGL * N_Element integrands. + + ''' + shape_u_n = utils.shape(u_n) + + # The coefficients of dLp / d\xi + diff_lag_coeff = params.dl_dxi_coeffs + + lobatto_nodes = params.lobatto_quadrature_nodes + Lobatto_weights = params.lobatto_weights_quadrature + + nodes_tile = af.transpose(af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1])) + power = af.flip(af.range(diff_lag_coeff.shape[1])) + power_tile = af.tile(power, 1, params.N_quad) + nodes_power = nodes_tile ** power_tile + weights_tile = af.transpose(af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1])) + nodes_weight = nodes_power * weights_tile + + dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight) + + + # The first option to calculate the volume integral term, directly uses + # the Lobatto quadrature instead of using the integrate() function by + # passing the coefficients of the Lagrange interpolated polynomial. + if(params.volume_integral_scheme == 'lobatto_quadrature' \ + and params.N_quad == params.N_LGL): + + # Flux using u_n, reordered to 1 X N_LGL X N_Elements array. + F_u_n = af.reorder(flux_x(u_n), 3, 0, 1, 2) + F_u_n = af.tile(F_u_n, d0 = params.N_LGL) + + # Multiplying with dLp / d\xi + integral_expansion = af.broadcast(utils.multiply, + dLp_dxi, F_u_n) + + # # Using the quadrature rule. + flux_integral = af.sum(integral_expansion, 1) + + flux_integral = af.reorder(flux_integral, 0, 2, 3, 1) + + # Using the integrate() function to calculate the volume integral term + # by passing the Lagrange interpolated polynomial. + else: + #print('option3') + analytical_flux_coeffs = af.transpose(af.moddims(u_n, + d0 = params.N_LGL, + d1 = params.N_Elements \ + * shape_u_n[2])) + + analytical_flux_coeffs = flux_x( + lagrange.lagrange_interpolation(analytical_flux_coeffs)) + analytical_flux_coeffs = af.transpose( + af.moddims(af.transpose(analytical_flux_coeffs), + d0 = params.N_LGL, d1 = params.N_Elements, + d2 = shape_u_n[2])) + + analytical_flux_coeffs = af.reorder(analytical_flux_coeffs, + d0 = 3, d1 = 1, d2 = 0, d3 = 2) + analytical_flux_coeffs = af.tile(analytical_flux_coeffs, + d0 = params.N_LGL) + analytical_flux_coeffs = af.moddims( + af.transpose(analytical_flux_coeffs), + d0 = params.N_LGL, + d1 = params.N_LGL * params.N_Elements, d2 = 1, + d3 = shape_u_n[2]) + + analytical_flux_coeffs = af.moddims( + analytical_flux_coeffs, d0 = params.N_LGL, + d1 = params.N_LGL * params.N_Elements * shape_u_n[2], + d2 = 1, d3 = 1) + + analytical_flux_coeffs = af.transpose(analytical_flux_coeffs) + + dl_dxi_coefficients = af.tile(af.tile(params.dl_dxi_coeffs, + d0 = params.N_Elements), \ + d0 = shape_u_n[2]) + + volume_int_coeffs = utils.poly1d_product(dl_dxi_coefficients, + analytical_flux_coeffs) + + flux_integral = lagrange.integrate(volume_int_coeffs) + flux_integral = af.moddims(af.transpose(flux_integral), + d0 = params.N_LGL, + d1 = params.N_Elements, + d2 = shape_u_n[2]) + + return flux_integral + + + +def volume_integral_flux_u_n_flux_n(u_n, flux_n): + ''' + Calculates the volume integral of flux in the wave equation. + + :math:`\\int_{-1}^1 f(u) \\frac{d L_p}{d\\xi} d\\xi` + + This will give N values of flux integral as p varies from 0 to N - 1. + + This integral is carried out using the analytical form of the integrand + obtained as a linear combination of Lagrange basis polynomials. + + This integrand is the used in the integrate() function. + + Calculation of volume integral flux using N_LGL Lobatto quadrature points + can be vectorized and is much faster. + + Parameters + ---------- + u : arrayfire.Array [N_LGL N_Elements 1 1] Amplitude of the wave at the mapped LGL nodes of each element. @@ -390,7 +524,6 @@ def volume_integral_flux_u_n_flux_n(u_n, flux_n): def lax_friedrichs_flux(u_n): ''' - Calculates the lax-friedrichs_flux :math:`f_i` using. :math:`f_i = \\frac{F(u^{i + 1}_0) + F(u^i_{N_{LGL} - 1})}{2} - \\frac @@ -605,7 +738,7 @@ def b_vector(u_n): .. _Report: https://goo.gl/sNsXXK ''' - volume_integral = volume_integral_flux(u_n) + volume_integral = volume_integral_flux_multiple_u_n(u_n) Surface_term = surface_term(u_n) b_vector_array = (volume_integral - Surface_term) @@ -842,7 +975,7 @@ def time_evolution(): # * delta_t # Implementing RK 4 scheme - u += RK4_timestepping_u_n_flux_n(A_inverse, u, flux_x(u), delta_t) + u += RK4_timestepping(A_inverse, u, delta_t) # Implementing RK 6 scheme #u += RK6_timestepping(A_inverse, u, delta_t) diff --git a/examples/maxwells_equations/maxwell's_equations_1d.ipynb b/examples/maxwells_equations/maxwells_equations_1d.ipynb similarity index 100% rename from examples/maxwells_equations/maxwell's_equations_1d.ipynb rename to examples/maxwells_equations/maxwells_equations_1d.ipynb diff --git a/examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb b/examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb new file mode 100644 index 0000000..93a2617 --- /dev/null +++ b/examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb @@ -0,0 +1,372 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1193: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n", + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1220: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n" + ] + } + ], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../../'))\n", + "\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "import arrayfire as af\n", + "\n", + "from dg_maxwell import params\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import wave_equation as w1d\n", + "from dg_maxwell import utils\n", + "\n", + "af.set_backend('opencl')\n", + "af.set_device(1)\n", + "af.info()\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Set the initial conditions\n", + "\n", + "E_00 = 1.\n", + "E_01 = 1.\n", + "\n", + "B_00 = 0.2\n", + "B_01 = 0.5\n", + "\n", + "E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + E_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + B_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2)\n", + "u_init[:, :, 0] = E_z_init\n", + "u_init[:, :, 1] = E_z_init" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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l1SEREUWcw4cPo7CwcML7du7cCavVipqamgBHNTEmFSjkPPnKKbT1DmFJVhK+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dsOI+bDed8xnei0eX1+PtqlNcexSkUFEYl9RWc4e8IB3vk5g6rfZVBOKl6/zfLdaoEQ4KPfwbon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\n6+AmIhISCW4X35w3EoCH3ttFY3uX4UTRw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "element_LGL_flat = af.flat(params.element_LGL)\n", + "E_z_init_flat = af.flat(u_init[:, :, 0])\n", + "B_y_init_flat = af.flat(u_init[:, :, 1])\n", + "\n", + "plt.plot(element_LGL_flat, E_z_init_flat, label = r'$E_z$')\n", + "plt.plot(element_LGL_flat, B_y_init_flat, label = r'$B_y$')\n", + "\n", + "plt.title(r'Plot of $E_z(t = 0)$ and $B_y(t = 0)$')\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "\n", + "plt.legend(prop={'size': 14})\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Formal implementation of volume integral flux for multiple-u's" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "option3\n" + ] + } + ], + "source": [ + "# 2. Check if the volume term works for multiple u's.\n", + "\n", + "u_n = u_init[:, :, :].copy()\n", + "\n", + "\n", + "shape_u_n = utils.shape(u_n)\n", + "# The coefficients of dLp / d\\xi\n", + "diff_lag_coeff = params.dl_dxi_coeffs\n", + "\n", + "lobatto_nodes = params.lobatto_quadrature_nodes\n", + "Lobatto_weights = params.lobatto_weights_quadrature\n", + "\n", + "nodes_tile = af.transpose(af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1]))\n", + "power = af.flip(af.range(diff_lag_coeff.shape[1]))\n", + "power_tile = af.tile(power, 1, params.N_quad)\n", + "nodes_power = nodes_tile ** power_tile\n", + "weights_tile = af.transpose(af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1]))\n", + "nodes_weight = nodes_power * weights_tile\n", + "\n", + "dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight)\n", + "\n", + "\n", + "# The first option to calculate the volume integral term, directly uses\n", + "# the Lobatto quadrature instead of using the integrate() function by\n", + "# passing the coefficients of the Lagrange interpolated polynomial.\n", + "if(params.volume_integral_scheme == 'lobatto_quadrature' \\\n", + " and params.N_quad == params.N_LGL):\n", + "\n", + " # Flux using u_n, reordered to 1 X N_LGL X N_Elements array.\n", + " F_u_n = af.reorder(w1d.flux_x(u_n), 3, 0, 1, 2)\n", + " F_u_n = af.tile(F_u_n, d0 = params.N_LGL)\n", + "\n", + " # Multiplying with dLp / d\\xi\n", + " integral_expansion = af.broadcast(utils.multiply,\n", + " dLp_dxi, F_u_n)\n", + "\n", + "# # Using the quadrature rule.\n", + " flux_integral = af.sum(integral_expansion, 1)\n", + "\n", + " flux_integral = af.reorder(flux_integral, 0, 2, 3, 1)\n", + "\n", + "# Using the integrate() function to calculate the volume integral term\n", + "# by passing the Lagrange interpolated polynomial.\n", + "else:\n", + " print('option3')\n", + " analytical_flux_coeffs = af.transpose(af.moddims(u_n,\n", + " d0 = params.N_LGL,\n", + " d1 = params.N_Elements * shape_u_n[2]))\n", + " \n", + " analytical_flux_coeffs = w1d.flux_x(lagrange.lagrange_interpolation(analytical_flux_coeffs))\n", + " analytical_flux_coeffs = af.transpose(af.moddims(af.transpose(analytical_flux_coeffs),\n", + " d0 = params.N_LGL, d1 = params.N_Elements,\n", + " d2 = shape_u_n[2]))\n", + " \n", + " analytical_flux_coeffs = af.reorder(analytical_flux_coeffs, d0 = 3, d1 = 1, d2 = 0, d3 = 2)\n", + " analytical_flux_coeffs = af.tile(analytical_flux_coeffs, d0 = params.N_LGL)\n", + " analytical_flux_coeffs = af.moddims(af.transpose(analytical_flux_coeffs), d0 = params.N_LGL,\n", + " d1 = params.N_LGL * params.N_Elements, d2 = 1,\n", + " d3 = shape_u_n[2])\n", + " analytical_flux_coeffs = af.moddims(analytical_flux_coeffs, d0 = params.N_LGL,\n", + " d1 = params.N_LGL * params.N_Elements * shape_u_n[2],\n", + " d2 = 1,\n", + " d3 = 1)\n", + " analytical_flux_coeffs = af.transpose(analytical_flux_coeffs)\n", + "\n", + " dl_dxi_coefficients = af.tile(af.tile(params.dl_dxi_coeffs, d0 = params.N_Elements), d0 = shape_u_n[2])\n", + "\n", + " volume_int_coeffs = utils.poly1d_product(dl_dxi_coefficients,\n", + " analytical_flux_coeffs)\n", + " \n", + " flux_integral = lagrange.integrate(volume_int_coeffs)\n", + " flux_integral = af.moddims(af.transpose(flux_integral), d0 = params.N_LGL,\n", + " d1 = params.N_Elements,\n", + " d2 = shape_u_n[2])\n", + "\n", + "# flux_integral = af.moddims(flux_integral, params.N_LGL, params.N_Elements)\n", + "\n", + "flux_integral_test = flux_integral.copy()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Testing" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "u_n = u_init[:, :, 0].copy()\n", + "\n", + "flux_integral_ref = w1d.volume_integral_flux(u_n)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n" + ] + } + ], + "source": [ + "print(af.all_true(af.abs(flux_integral_ref - flux_integral_test[:, :, 0]) < 1e-13))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [], + "source": [ + "foo = af.moddims(af.range(params.N_LGL * params.N_Elements), d0 = params.N_LGL, d1 = params.N_Elements)\n", + "foo = af.tile(foo, d0 = 1, d1 = 1, d2 = 2)\n", + "\n", + "# print(foo)\n", + "\n", + "foo_elements_joined = af.transpose(af.moddims(foo, d0 = params.N_LGL,\n", + " d1 = params.N_Elements * foo.shape[2]))\n", + "\n", + "# print(foo_elements_joined)\n", + "\n", + "foo_interpolate = lagrange.lagrange_interpolation(foo_elements_joined)\n", + "foo_interpolate_elements_separate = af.transpose(af.moddims(af.transpose(foo_interpolate), d0 = params.N_LGL,\n", + " d1 = params.N_Elements, d2 = foo.shape[2]))\n", + "\n", + "# print(foo_interpolate_elements_separate)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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R3lH4a95YuJOagse4fvha7h89h4NHBydZkIhkQt4mIkJJhmk1TBkqsbBgimmC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\n6VNw39Ww7nl46Acw5czUiSRJKTz/EKxZDjtU87F//zp717ayuqGZUUO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r4LBzUqeRJEl5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\nMdU2NGP37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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def function(xi):\n", + " return af.sin(np.pi * xi)\n", + "\n", + "# Test lagrange interpolation\n", + "\n", + "f_i = function(params.xi_LGL)\n", + "fn_i = af.transpose(af.tile(f_i, d0 = 1, d1 = 1))\n", + "\n", + "lagrange_interpolation = lagrange.lagrange_interpolation(fn_i)\n", + "\n", + "# Testing\n", + "\n", + "xi_linsp = utils.linspace(-1, 1, 30)\n", + "function_analytical = function(xi_linsp)\n", + "\n", + "function_interpolated_xi_linsp = utils.polyval_1d(lagrange_interpolation, xi_linsp)\n", + "\n", + "plt.plot(np.array(xi_linsp), np.array(function_analytical), 'o', label = 'Analytical function')\n", + "plt.plot(np.array(xi_linsp), np.array(af.transpose(function_interpolated_xi_linsp[0])), '--',\n", + " label = 'Interpolated')\n", + "\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Plot of analytical function and interpolated functions.')\n", + "plt.legend(prop={'size': 14})\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 6923432d7f437f883ecdd78d11d6ca58e20976bd Mon Sep 17 00:00:00 2001 From: AAT Date: Sat, 9 Dec 2017 17:00:04 +0530 Subject: [PATCH 04/13] Removed the functions which took flux as an argument. --- dg_maxwell/tests/test_waveEqn.py | 133 --------- dg_maxwell/wave_equation.py | 260 ------------------ ...nb => advection_1d_multiple_u_and_f.ipynb} | 14 +- 3 files changed, 7 insertions(+), 400 deletions(-) rename examples/maxwells_equations/{maxwells_equations_vetorised_flux.ipynb => advection_1d_multiple_u_and_f.ipynb} (99%) diff --git a/dg_maxwell/tests/test_waveEqn.py b/dg_maxwell/tests/test_waveEqn.py index 2532fdc..ca33465 100644 --- a/dg_maxwell/tests/test_waveEqn.py +++ b/dg_maxwell/tests/test_waveEqn.py @@ -430,64 +430,6 @@ def test_volume_integral_flux_multiple_u_n(): -def test_volume_integral_flux_u_n_flux_n(): - ''' - A test function to check the volume_integral_flux function in wave_equation - module by analytically calculated Gauss-Lobatto quadrature. - - Reference - --------- - The link to the sage worksheet where the calculations were caried out is - given below. - `https://goo.gl/5Mub8M` - ''' - threshold = 4e-9 - params.c = 1 - change_parameters(8, 10, 11, 'gaussian') - - referenceFluxIntegral = af.transpose(af.interop.np_to_af_array(np.array - ([ - [-0.002016634876668093, -0.000588597708116113, -0.0013016773719126333,\ - -0.002368387579324652, -0.003620502047659841, -0.004320197094090966, - -0.003445512010153811, 0.0176615086879261],\ - - [-0.018969769374, -0.00431252844519,-0.00882630935977,-0.0144355176966,\ - -0.019612124119, -0.0209837936827, -0.0154359890788, 0.102576031756], \ - - [-0.108222418798, -0.0179274222595, -0.0337807018822, -0.0492589052599,\ - -0.0588472807471, -0.0557970236273, -0.0374764132459, 0.361310165819],\ - - [-0.374448714304, -0.0399576371245, -0.0683852285846, -0.0869229749357,\ - -0.0884322503841, -0.0714664112839, -0.0422339853622, 0.771847201979], \ - - [-0.785754362849, -0.0396035640187, -0.0579313769517, -0.0569022801117,\ - -0.0392041960688, -0.0172295769141, -0.00337464521455, 1.00000000213],\ - - [-1.00000000213, 0.00337464521455, 0.0172295769141, 0.0392041960688,\ - 0.0569022801117, 0.0579313769517, 0.0396035640187, 0.785754362849],\ - - [-0.771847201979, 0.0422339853622, 0.0714664112839, 0.0884322503841, \ - 0.0869229749357, 0.0683852285846, 0.0399576371245, 0.374448714304],\ - - [-0.361310165819, 0.0374764132459, 0.0557970236273, 0.0588472807471,\ - 0.0492589052599, 0.0337807018822, 0.0179274222595, 0.108222418798], \ - - [-0.102576031756, 0.0154359890788, 0.0209837936827, 0.019612124119, \ - 0.0144355176966, 0.00882630935977, 0.00431252844519, 0.018969769374],\ - - [-0.0176615086879, 0.00344551201015 ,0.00432019709409, 0.00362050204766,\ - 0.00236838757932, 0.00130167737191, 0.000588597708116, 0.00201663487667]\ - - ]))) - - numerical_flux = wave_equation.volume_integral_flux_u_n_flux_n( - params.u[:, :, 0], - wave_equation.flux_x(params.u[:, :, 0])) - - assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) - - - def test_lax_friedrichs_flux(): ''' A test function to test the lax_friedrichs_flux function in wave_equation @@ -503,22 +445,6 @@ def test_lax_friedrichs_flux(): -def test_lax_friedrichs_flux_u_n_flux_n(): - ''' - A test function to test the lax_friedrichs_flux function in wave_equation - module. - ''' - threshold = 1e-14 - - params.c = 1 - - f_i = wave_equation.lax_friedrichs_flux_u_n_flux_n(params.u[:, :, 0], - wave_equation.flux_x( - params.u[:, :, 0])) - analytical_lax_friedrichs_flux = params.u[-1, :, 0] - assert af.max(af.abs(analytical_lax_friedrichs_flux - f_i)) < threshold - - def test_surface_term(): ''' A test function to test the surface_term function in the wave_equation @@ -548,38 +474,6 @@ def test_surface_term(): -def test_surface_term_u_n_flux_n(): - ''' - A test function to test the surface_term function in the wave_equation - module using analytical Lax-Friedrichs flux. - ''' - threshold = 1e-13 - params.c = 1 - - change_parameters(8, 10, 8, 'gaussian') - - analytical_f_i = (params.u[-1, :, 0]) - analytical_f_i_minus1 = (af.shift(params.u[-1, :, 0], 0, 1)) - - L_p_1 = af.constant(0, params.N_LGL, dtype = af.Dtype.f64) - L_p_1[params.N_LGL - 1] = 1 - - L_p_minus1 = af.constant(0, params.N_LGL, dtype = af.Dtype.f64) - L_p_minus1[0] = 1 - - analytical_surface_term = af.blas.matmul(L_p_1, analytical_f_i)\ - - af.blas.matmul(L_p_minus1, analytical_f_i_minus1) - - numerical_surface_term = wave_equation.surface_term_u_n_flux_n( - params.u[:, :, 0], - wave_equation.lax_friedrichs_flux(params.u[:, :, 0])) - - assert af.max(af.abs(analytical_surface_term - numerical_surface_term)) \ - < threshold - return analytical_surface_term - - - def test_b_vector(): ''' A test function to check the b vector obtained analytically and compare it @@ -601,33 +495,6 @@ def test_b_vector(): assert (b_vector_analytical - b_vector_array) < threshold -def test_b_vector_u_n_flux_n(): - ''' - A test function to check the b vector obtained analytically and compare it - with the one returned by b_vector function in wave_equation module. - ''' - threshold = 1e-13 - params.c = 1 - - change_parameters(8, 10, 8, 'gaussian') - - u_n_A_matrix = af.blas.matmul(wave_equation.A_matrix(), - params.u[:, :, 0]) - volume_integral_flux = wave_equation.volume_integral_flux_u_n_flux_n( - params.u[:, :, 0], wave_equation.flux_x(params.u[:, :, 0])) - - surface_term = test_surface_term_u_n_flux_n() - - b_vector_analytical = u_n_A_matrix \ - + (volume_integral_flux - surface_term) \ - * params.delta_t - - b_vector_array = wave_equation.b_vector_u_n_flux_n( - params.u[:, :, 0], wave_equation.flux_x(params.u[:, :, 0])) - - assert (b_vector_analytical - b_vector_array) < threshold - - def test_integrate(): ''' diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 9f144cc..e197ba3 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -429,99 +429,6 @@ def volume_integral_flux_multiple_u_n(u_n): -def volume_integral_flux_u_n_flux_n(u_n, flux_n): - ''' - Calculates the volume integral of flux in the wave equation. - - :math:`\\int_{-1}^1 f(u) \\frac{d L_p}{d\\xi} d\\xi` - - This will give N values of flux integral as p varies from 0 to N - 1. - - This integral is carried out using the analytical form of the integrand - obtained as a linear combination of Lagrange basis polynomials. - - This integrand is the used in the integrate() function. - - Calculation of volume integral flux using N_LGL Lobatto quadrature points - can be vectorized and is much faster. - - Parameters - ---------- - - u : arrayfire.Array [N_LGL N_Elements 1 1] - Amplitude of the wave at the mapped LGL nodes of each element. - - flux_n : arrayfire:Array [N_LGL N_Elements 1 1] - Flux of the wave at the mapped LGL nodes of each element. - - Returns - ------- - - flux_integral : arrayfire.Array [N_LGL N_Elements 1 1] - Value of the volume integral flux. It contains the integral - of all N_LGL * N_Element integrands. - - ''' - # The coefficients of dLp / d\xi - diff_lag_coeff = params.dl_dxi_coeffs - - lobatto_nodes = params.lobatto_quadrature_nodes - Lobatto_weights = params.lobatto_weights_quadrature - - nodes_tile = af.transpose(af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1])) - power = af.flip(af.range(diff_lag_coeff.shape[1])) - power_tile = af.tile(power, 1, params.N_quad) - nodes_power = nodes_tile ** power_tile - weights_tile = af.transpose(af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1])) - nodes_weight = nodes_power * weights_tile - - dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight) - - - # The first option to calculate the volume integral term, directly uses - # the Lobatto quadrature instead of using the integrate() function by - # passing the coefficients of the Lagrange interpolated polynomial. - if(params.volume_integral_scheme == 'lobatto_quadrature' \ - and params.N_quad == params.N_LGL): - - # Flux using u_n, reordered to 1 X N_LGL X N_Elements array. - F_u_n = af.reorder(flux_n, 2, 0, 1) - - # Multiplying with dLp / d\xi - integral_expansion = af.broadcast(utils.multiply, - dLp_dxi, F_u_n) - - # Using the quadrature rule. - flux_integral = af.sum(integral_expansion, 1) - flux_integral = af.reorder(flux_integral, 0, 2, 1) - - # Using the integrate() function to calculate the volume integral term - # by passing the Lagrange interpolated polynomial. - else: - #print('option3') - analytical_flux_coeffs = lagrange.lagrange_interpolation_u(flux_n) - - analytical_flux_coeffs = af.reorder(analytical_flux_coeffs, 1, 0, 2) - - dl_dxi_coefficients = af.reorder(params.dl_dxi_coeffs, 1, 0) - - # The product of polynomials is calculated using af.convolve1 - volume_int_coeffs = af.convolve1(dl_dxi_coefficients, - analytical_flux_coeffs, - conv_mode=af.CONV_MODE.EXPAND) - volume_int_coeffs = af.reorder(volume_int_coeffs, 1, 2, 0) - volume_int_coeffs = af.moddims(volume_int_coeffs, - params.N_LGL * params.N_Elements, - 2 * params.N_LGL - 2) - - flux_integral = lagrange.integrate(volume_int_coeffs) - flux_integral = af.moddims(flux_integral, params.N_LGL, params.N_Elements) - - - return flux_integral - - - def lax_friedrichs_flux(u_n): ''' Calculates the lax-friedrichs_flux :math:`f_i` using. @@ -562,54 +469,6 @@ def lax_friedrichs_flux(u_n): -def lax_friedrichs_flux_u_n_flux_n(u_n, flux_n): - ''' - - Calculates the lax-friedrichs_flux :math:`f_i` using. - - :math:`f_i = \\frac{F(u^{i + 1}_0) + F(u^i_{N_{LGL} - 1})}{2} - \\frac - {\Delta x}{2\Delta t} (u^{i + 1}_0 - u^i_{N_{LGL} - 1})` - - The algorithm used is explained in this `document`_ - - .. _document: `https://goo.gl/sNsXXK` - - - Parameters - ---------- - - u_n : arrayfire.Array [N_LGL N_Elements 1 1] - Amplitude of the wave at the mapped LGL nodes of each element. - - f_n : arrayfire:Array [N_LGL N_Elements 1 1] - Flux of the wave at the mapped LGL nodes of each element. - - Returns - ------- - - boundary_flux : arrayfire.Array [1 N_Elements 1 1] - Contains the value of the flux at the boundary elements. - Periodic boundary conditions are used. - - ''' - - u_iplus1_0 = af.shift(u_n[0, :], 0, -1) - flux_iplus1_0 = af.shift(u_n[0, :], 0, -1) - - u_i_N_LGL = u_n[-1, :] - flux_i_N_LGL = flux_n[-1, :] - - flux_iplus1_0 = flux_x(u_iplus1_0) - flux_i_N_LGL = flux_x(u_i_N_LGL) - - boundary_flux = (flux_iplus1_0 + flux_i_N_LGL) / 2 \ - - params.c_lax * (u_iplus1_0 - u_i_N_LGL) / 2 - - - return boundary_flux - - - def analytical_u_LGL(t_n): ''' @@ -674,46 +533,6 @@ def surface_term(u_n): return surface_term -def surface_term_u_n_flux_n(u_n, LF_flux_i): - ''' - - Calculates the surface term, - :math:`L_p(1) f_i - L_p(-1) f_{i - 1}` - using the lax_friedrichs_flux function and lagrange_basis_value - from params module. - - Parameters - ---------- - u_n : arrayfire.Array [N_LGL N_Elements 1 1] - Amplitude of the wave at the mapped LGL nodes of each element. - - flux_n : af.Array [N_LGL N_Elements 1 1] - Lax Friedrichs flux of the wave at the mapped LGL nodes of each element. - - Returns - ------- - surface_term : arrayfire.Array [N_LGL N_Elements 1 1] - The surface term represented in the form of an array, - :math:`L_p (1) f_i - L_p (-1) f_{i - 1}`, where p varies - from zero to :math:`N_{LGL}` and i from zero to - :math:`N_{Elements}`. p varies along the rows and i along - columns. - - **See:** `PDF`_ describing the algorithm to obtain the surface term. - - .. _PDF: https://goo.gl/Nhhgzx - - ''' - - L_p_minus1 = params.lagrange_basis_value[:, 0] - L_p_1 = params.lagrange_basis_value[:, -1] - LF_flus_iminus1 = af.shift(LF_flux_i, 0, 1) - surface_term = af.blas.matmul(L_p_1, LF_flux_i) \ - - af.blas.matmul(L_p_minus1, LF_flus_iminus1) - - return surface_term - - def b_vector(u_n): ''' @@ -746,44 +565,6 @@ def b_vector(u_n): -# 5. Modify the b vector to accept the flux as an argument - -def b_vector_u_n_flux_n(u_n, flux_n): - ''' - - Calculates the b vector for N_Elements number of elements. - - Parameters - ---------- - - u_n : arrayfire.Array [N_LGL N_Elements 1 1] - Amplitude of the wave at the mapped LGL nodes of each element. - - flux_n : af.Array [N_LGL N_Elements 1 1] - Flux of the wave at the mapped LGL nodes of each element. - - Returns - ------- - - b_vector_array : arrayfire.Array [N_LGL N_Elements 1 1] - Contains the b vector(of shape [N_LGL 1 1 1]) - for each element. - - **See:** `Report`_ for the b-vector can be found here - - .. _Report: https://goo.gl/sNsXXK - - ''' - volume_integral = volume_integral_flux_u_n_flux_n(u_n, flux_n) - Surface_term = surface_term_u_n_flux_n( - u_n, - lax_friedrichs_flux_u_n_flux_n(u_n, flux_n)) - - b_vector_array = (volume_integral - Surface_term) - - return b_vector_array - - def RK4_timestepping(A_inverse, u, delta_t): ''' @@ -820,47 +601,6 @@ def RK4_timestepping(A_inverse, u, delta_t): -def RK4_timestepping_u_n_flux_n(A_inverse, u, flux, delta_t): - ''' - - Implementing the Runge-Kutta (RK4) method to evolve the wave. - - Parameters - ---------- - A_inverse : arrayfire.Array[N_LGL N_LGL 1 1] - The inverse of the A matrix which was calculated - using A_matrix() function. - - u : arrayfire.Array[N_LGL N_Elements 1 1] - u at the mapped LGL points - - flux : af.Array [N_LGL N_Elements 1 1] - Flux of the wave at the mapped LGL nodes of each element. - - delta_t : float64 - The time-step by which u is to be evolved. - - Returns - ------- - delta_u : arrayfire.Array [N_LGL N_Elements 1 1] - The change in u at the mapped LGL points. - - ''' - - k1 = af.matmul(A_inverse, b_vector_u_n_flux_n(u, flux_x(u))) - k2 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k1 * delta_t / 2, - flux_x(u + k1 * delta_t / 2))) - k3 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k2 * delta_t / 2, - flux_x(u + k2 * delta_t / 2))) - k4 = af.matmul(A_inverse, b_vector_u_n_flux_n(u + k3 * delta_t, - flux_x(u + k3 * delta_t))) - - delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6 - - return delta_u - - - def RK6_timestepping(A_inverse, u, delta_t): ''' diff --git a/examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb b/examples/maxwells_equations/advection_1d_multiple_u_and_f.ipynb similarity index 99% rename from examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb rename to examples/maxwells_equations/advection_1d_multiple_u_and_f.ipynb index 93a2617..d541bb3 100644 --- a/examples/maxwells_equations/maxwells_equations_vetorised_flux.ipynb +++ b/examples/maxwells_equations/advection_1d_multiple_u_and_f.ipynb @@ -223,13 +223,6 @@ "flux_integral_test = flux_integral.copy()" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, { "cell_type": "markdown", "metadata": {}, @@ -272,6 +265,13 @@ "outputs": [], "source": [] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Miscellaneous tests for the modules" + ] + }, { "cell_type": "code", "execution_count": 40, From baac2d04ba4d324ad5c37e0d43dfc73e414790b1 Mon Sep 17 00:00:00 2001 From: AAT Date: Sat, 9 Dec 2017 19:08:33 +0530 Subject: [PATCH 05/13] Time evolution happening for multiple u and it's working --- dg_maxwell/params.py | 18 +- dg_maxwell/tests/utils/test_utils.py | 73 +++ dg_maxwell/utils.py | 31 + dg_maxwell/wave_equation.py | 124 +++- examples/1D_wave_equation_solver.ipynb | 122 +++- .../advec_1d_multiple_u_LF_flux.ipynb | 199 +++++++ .../advec_1d_multiple_u_RK4.ipynb | 541 ++++++++++++++++++ .../advec_1d_multiple_u_surface_term.ipynb | 256 +++++++++ ... => advec_1d_multiple_u_volume_term.ipynb} | 0 main.py | 22 +- 10 files changed, 1362 insertions(+), 24 deletions(-) create mode 100644 dg_maxwell/tests/utils/test_utils.py create mode 100644 examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb create mode 100644 examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb create mode 100644 examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb rename examples/maxwells_equations/{advection_1d_multiple_u_and_f.ipynb => advec_1d_multiple_u_volume_term.ipynb} (100%) diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index 3620f34..8f58d03 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -32,7 +32,7 @@ N_quad = 8 # Wave speed. -c = 0.5 +c = -1. # The total time for which the wave is to be evolved by the simulation. total_time = 2.01 @@ -115,6 +115,22 @@ # Initializing the amplitudes. Change u_init to required initial conditions. if (wave=='sin'): + #E_00 = 1. + #E_01 = 1. + + #B_00 = 0.2 + #B_01 = 0.5 + + #E_z_init = E_00 * af.sin(2 * np.pi * element_LGL) \ + #+ E_01 * af.cos(2 * np.pi * element_LGL) + + #B_y_init = B_00 * af.sin(2 * np.pi * element_LGL) \ + #+ B_01 * af.cos(2 * np.pi * element_LGL) + + #u_init = af.constant(0., d0 = N_LGL, d1 = N_Elements, + #d2 = 2, dtype = af.Dtype.f64) + #u_init[:, :, 0] = E_z_init + #u_init[:, :, 1] = B_y_init u_init = af.sin(2 * np.pi * element_LGL) if (wave=='gaussian'): diff --git a/dg_maxwell/tests/utils/test_utils.py b/dg_maxwell/tests/utils/test_utils.py new file mode 100644 index 0000000..07b0394 --- /dev/null +++ b/dg_maxwell/tests/utils/test_utils.py @@ -0,0 +1,73 @@ +#! /usr/bin/env python3 +# -*- coding: utf-8 -*- + +import numpy as np +import arrayfire as af + +from dg_maxwell import params +from dg_maxwell import utils +from dg_maxwell import lagrange + +af.set_backend('opencl') +af.set_device(1) + +def test_matmul_3D(): + ''' + ''' + M = 3 + N = 2 + P = 4 + Q = 2 + + a = af.range(M * N * Q, dtype = af.Dtype.u32) + b = af.range(N * P * Q, dtype = af.Dtype.u32) + + a = af.moddims(a, d0 = M, d1 = N, d2 = Q) + b = af.moddims(b, d0 = N, d1 = P, d2 = Q) + + a_init = a + b_init = b + + ref_a_0 = np.matmul(np.array(a_init[:, :, 0]), + np.array(b_init[:, :, 0])) + + ref_a_1 = np.matmul(np.array(a_init[:, :, 1]), + np.array(b_init[:, :, 1])) + + test_matmul = np.array(utils.matmul_3D(a, b)) + + diff_mat_0 = np.abs(test_matmul[:, :, 0] - ref_a_0) + diff_mat_1 = np.abs(test_matmul[:, :, 1] - ref_a_1) + + assert np.all(diff_mat_0 == 0) and np.all(diff_mat_1 == 0) + + + +def test_poly1d_prod(): + ''' + Checks the product of the polynomials of different degrees using the + poly1d_product function and compares it to the analytically calculated + product coefficients. + ''' + + N = 3 + + N_a = 3 + poly_a = af.range(N * N_a, dtype = af.Dtype.u32) + poly_a = af.moddims(poly_a, d0 = N, d1 = N_a) + + N_b = 2 + poly_b = af.range(N * N_b, dtype = af.Dtype.u32) + poly_b = af.moddims(poly_b, d0 = N, d1 = N_b) + + ref_poly = af.np_to_af_array(np.array([[0., 0., 9., 18.], + [1., 8., 23., 28.], + [4., 20., 41., 40.]])) + + test_poly1d_prod = utils.poly1d_product(poly_a, poly_b) + test_poly1d_prod_commutative = utils.poly1d_product(poly_b, poly_a) + + diff = af.abs(test_poly1d_prod - ref_poly) + diff_commutative = af.abs(test_poly1d_prod_commutative - ref_poly) + + assert af.all_true(diff == 0.) and af.all_true(diff_commutative == 0.) diff --git a/dg_maxwell/utils.py b/dg_maxwell/utils.py index 42bee16..d66388a 100644 --- a/dg_maxwell/utils.py +++ b/dg_maxwell/utils.py @@ -228,3 +228,34 @@ def poly1d_product(poly_a, poly_b): return af.transpose(af.convolve1(af.transpose(poly_a), af.transpose(poly_b), conv_mode = af.CONV_MODE.EXPAND)) + + +def matmul_3D(a, b): + ''' + Finds the matrix multiplication of :math:`Q` pairs of matrices ``a`` and + ``b``. + Parameters + ---------- + a : af.Array [M N Q 1] + First set of :math:`Q` 2D arrays :math:`N \\neq 1` and :math:`M \\neq 1`. + b : af.Array [N P Q 1] + Second set of :math:`Q` 2D arrays :math:`P \\neq 1`. + Returns + ------- + matmul : af.Array [M P Q 1] + Matrix multiplication of :math:`Q` sets of 2D arrays. + ''' + shape_a = shape(a) + shape_b = shape(b) + + P = shape_b[1] + + a = af.transpose(a) + a = af.reorder(a, d0 = 0, d1 = 3, d2 = 2, d3 = 1) + a = af.tile(a, d0 = 1, d1 = P) + b = af.tile(b, d0 = 1, d1 = 1, d2 = 1, d3 = a.shape[3]) + + matmul = af.sum(a * b, dim = 0) + matmul = af.reorder(matmul, d0 = 3, d1 = 1, d2 = 2, d3 = 0) + + return matmul \ No newline at end of file diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index e197ba3..0c80c8c 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -332,12 +332,12 @@ def volume_integral_flux_multiple_u_n(u_n): u : arrayfire.Array [N_LGL N_Elements M 1] Amplitude of the wave at the mapped LGL nodes of each element. This - function can computer flux for :math:`M` :math:`u` simultaneously. + function can computer flux for :math:`M` :math:`u`. Returns ------- - flux_integral : arrayfire.Array [N_LGL N_Elements 1 1] + flux_integral : arrayfire.Array [N_LGL N_Elements M 1] Value of the volume integral flux. It contains the integral of all N_LGL * N_Element integrands. @@ -444,8 +444,9 @@ def lax_friedrichs_flux(u_n): Parameters ---------- - u_n : arrayfire.Array [N_LGL N_Elements 1 1] + u_n : arrayfire.Array [N_LGL N_Elements M 1] Amplitude of the wave at the mapped LGL nodes of each element. + This code will work for :math:`M` multiple ``u_n``. Returns ------- @@ -489,8 +490,24 @@ def analytical_u_LGL(t_n): ''' time = t_n * params.delta_t - u_t_n = af.sin(2 * np.pi * (params.element_LGL - params.c * time)) + + #u_t_n = af.sin(2 * np.pi * (params.element_LGL - params.c * time)) + + # Multiple waves test + E_00 = 1. + E_01 = 1. + + B_00 = 0.2 + B_01 = 0.5 + E_z_t_n = E_00 * af.sin(2 * np.pi * (params.element_LGL - params.c * time))\ + + E_01 * af.cos(2 * np.pi * (params.element_LGL - params.c * time)) + + B_y_t_n = B_00 * af.sin(2 * np.pi * (params.element_LGL - params.c * time))\ + + B_01 * af.cos(2 * np.pi * (params.element_LGL - params.c * time)) + + u_t_n = B_y_t_n + return u_t_n @@ -534,6 +551,51 @@ def surface_term(u_n): +def surface_term_multiple_u(u_n): + ''' + + Calculates the surface term, + :math:`L_p(1) f_i - L_p(-1) f_{i - 1}` + using the lax_friedrichs_flux function and lagrange_basis_value + from params module. + + Parameters + ---------- + u_n : arrayfire.Array [N_LGL N_Elements M 1] + Amplitude of the wave at the mapped LGL nodes of each element. + This code will work for multiple :math:`M` ``u_n`` + + Returns + ------- + surface_term : arrayfire.Array [N_LGL N_Elements M 1] + The surface term represented in the form of an array, + :math:`L_p (1) f_i - L_p (-1) f_{i - 1}`, where p varies + from zero to :math:`N_{LGL}` and i from zero to + :math:`N_{Elements}`. p varies along the rows and i along + columns. + + **See:** `PDF`_ describing the algorithm to obtain the surface term. + + .. _PDF: https://goo.gl/Nhhgzx + + ''' + + shape_u_n = utils.shape(u_n) + + L_p_minus1 = af.tile(params.lagrange_basis_value[:, 0], + d0 = 1, d1 = 1, d2 = shape_u_n[2]) + L_p_1 = af.tile(params.lagrange_basis_value[:, -1], + d0 = 1, d1 = 1, d2 = shape_u_n[2]) + f_i = lax_friedrichs_flux(u_n) + f_iminus1 = af.shift(f_i, 0, 1) + + surface_term = utils.matmul_3D(L_p_1, f_i) \ + - utils.matmul_3D(L_p_minus1, f_iminus1) + + return surface_term + + + def b_vector(u_n): ''' @@ -558,7 +620,7 @@ def b_vector(u_n): ''' volume_integral = volume_integral_flux_multiple_u_n(u_n) - Surface_term = surface_term(u_n) + Surface_term = surface_term_multiple_u(u_n) b_vector_array = (volume_integral - Surface_term) return b_vector_array @@ -601,6 +663,39 @@ def RK4_timestepping(A_inverse, u, delta_t): +def RK4_timestepping_multiple_u(A_inverse, u, delta_t): + ''' + + Implementing the Runge-Kutta (RK4) method to evolve the wave. + + Parameters + ---------- + A_inverse : arrayfire.Array[N_LGL N_LGL 1 1] + The inverse of the A matrix which was calculated + using A_matrix() function. + + u : arrayfire.Array[N_LGL N_Elements M 1] + u at the mapped LGL points + + delta_t : float64 + The time-step by which u is to be evolved. + + Returns + ------- + delta_u : arrayfire.Array [N_LGL N_Elements 1 1] + The change in u at the mapped LGL points. + ''' + + k1 = utils.matmul_3D(A_inverse, b_vector(u)) + k2 = utils.matmul_3D(A_inverse, b_vector(u + k1 * delta_t / 2)) + k3 = utils.matmul_3D(A_inverse, b_vector(u + k2 * delta_t / 2)) + k4 = utils.matmul_3D(A_inverse, b_vector(u + k3 * delta_t)) + + delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6 + + return delta_u + + def RK6_timestepping(A_inverse, u, delta_t): ''' @@ -660,7 +755,7 @@ def RK6_timestepping(A_inverse, u, delta_t): -def time_evolution(): +def time_evolution(u = None): ''' Solves the wave equation @@ -690,22 +785,25 @@ def time_evolution(): os.makedirs(results_directory) - A_inverse = af.inverse(A_matrix()) element_LGL = params.element_LGL delta_t = params.delta_t - u = params.u_init + #u = params.u_init + shape_u_n = utils.shape(u) time = params.time + A_inverse = af.tile(af.inverse(A_matrix()), + d0 = 1, d1 = 1, + d2 = shape_u_n[2]) element_boundaries = af.np_to_af_array(params.np_element_array) - + for t_n in trange(0, time.shape[0]): # Storing u at timesteps which are multiples of 100. if (t_n % 20) == 0: h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') - dset = h5file.create_dataset('u_i', data = u, dtype = 'd') + dset = h5file.create_dataset('u_i', data = u[:, :, 1], dtype = 'd') - dset[:, :] = u[:, :] + dset[:, :] = u[:, :, 1] # # Implementing second order time-stepping. # u_n_plus_half = u + af.matmul(A_inverse, b_vector(u))\ @@ -715,14 +813,14 @@ def time_evolution(): # * delta_t # Implementing RK 4 scheme - u += RK4_timestepping(A_inverse, u, delta_t) + u += RK4_timestepping_multiple_u(A_inverse, u, delta_t) # Implementing RK 6 scheme #u += RK6_timestepping(A_inverse, u, delta_t) u_analytical = analytical_u_LGL(t_n + 1) - u_diff = af.abs(u - u_analytical) + u_diff = af.abs(u[:, :, 1] - u_analytical) return u_diff diff --git a/examples/1D_wave_equation_solver.ipynb b/examples/1D_wave_equation_solver.ipynb index 81d894c..3fdfc3c 100644 --- a/examples/1D_wave_equation_solver.ipynb +++ b/examples/1D_wave_equation_solver.ipynb @@ -59,7 +59,18 @@ "metadata": { "collapsed": true }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1193: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n", + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1220: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n" + ] + } + ], "source": [ "import os\n", "import sys\n", @@ -77,22 +88,115 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 15592/15592 [01:04<00:00, 243.23it/s]\n", - " 0%| | 0/15592 [00:00\n", + "Traceback (most recent call last):\n", + " File \"/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/arrayfire/array.py\", line 550, in __del__\n", + " backend.get().af_release_array(self.arr)\n", + "KeyboardInterrupt\n", + "\r", + " 26%|██▌ | 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"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mwave_equation\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime_evolution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/workspace/quazar/git/amanabt/DG_Maxwell/dg_maxwell/wave_equation.py\u001b[0m in \u001b[0;36mtime_evolution\u001b[0;34m()\u001b[0m\n\u001b[1;32m 762\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 763\u001b[0m \u001b[0;31m# Implementing RK 4 scheme\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 764\u001b[0;31m \u001b[0mu\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mRK4_timestepping\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA_inverse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m,\u001b[0m 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], @@ -126,7 +230,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.2" + "version": "3.6.3" } }, "nbformat": 4, diff --git a/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb new file mode 100644 index 0000000..4c687e3 --- /dev/null +++ b/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb @@ -0,0 +1,199 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1193: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n", + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1220: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n" + ] + } + ], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../../'))\n", + "\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "import arrayfire as af\n", + "\n", + "from dg_maxwell import params\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import wave_equation as w1d\n", + "from dg_maxwell import utils\n", + "\n", + "af.set_backend('opencl')\n", + "af.set_device(1)\n", + "af.info()\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Set the initial conditions\n", + "\n", + "E_00 = 1.\n", + "E_01 = 1.\n", + "\n", + "B_00 = 0.2\n", + "B_01 = 0.5\n", + "\n", + "E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + E_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + B_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2)\n", + "u_init[:, :, 0] = E_z_init\n", + "u_init[:, :, 1] = B_y_init" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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/znYkERHphY/ff4H5p58HoGLRj4gbnGg5Ue+ljhxL42fXU+PEML1hN9ue/7nt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\n0oVDL/+YSOPh45jLyZh1pe0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xREQ6VF52hCkNBQCMv/o+y2kkkNKu+jwA085voer0Cctp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\n0MjbFZ+Q4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "element_LGL_flat = af.flat(params.element_LGL)\n", + "E_z_init_flat = af.flat(u_init[:, :, 0])\n", + "B_y_init_flat = af.flat(u_init[:, :, 1])\n", + "\n", + "plt.plot(element_LGL_flat, E_z_init_flat, label = r'$E_z$')\n", + "plt.plot(element_LGL_flat, B_y_init_flat, label = r'$B_y$')\n", + "\n", + "plt.title(r'Plot of $E_z(t = 0)$ and $B_y(t = 0)$')\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "\n", + "plt.legend(prop={'size': 14})\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Prototype implementation of LF flux for multiple-u's" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "arrayfire.Array()\n", + "Type: float\n", + "\n", + "[1 10 2 1]\n", + " 0.6300 -0.1106 -0.6984 -0.3210 0.5000 0.6300 -0.1106 -0.6984 -0.3210 0.5000 \n", + "\n", + " 0.1724 -0.1435 -0.2610 -0.0179 0.2500 0.1724 -0.1435 -0.2610 -0.0179 0.2500 \n", + "\n", + "\n", + "\n" + ] + } + ], + "source": [ + "# Older LF flux code\n", + "u_n = u_init[:, :, :]\n", + "\n", + "u_iplus1_0 = af.shift(u_n[0, :], 0, -1)\n", + "u_i_N_LGL = u_n[-1, :]\n", + "flux_iplus1_0 = w1d.flux_x(u_iplus1_0)\n", + "flux_i_N_LGL = w1d.flux_x(u_i_N_LGL)\n", + "\n", + "boundary_flux = (flux_iplus1_0 + flux_i_N_LGL) / 2 \\\n", + " - params.c_lax * (u_iplus1_0 - u_i_N_LGL) / 2\n", + "\n", + "\n", + "print(boundary_flux)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# LF flux older code can handle multiple elements, no refactoring needed" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb new file mode 100644 index 0000000..3aeab5f --- /dev/null +++ b/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb @@ -0,0 +1,541 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1193: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n", + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1220: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n" + ] + } + ], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../../'))\n", + "\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "import arrayfire as af\n", + "\n", + "from dg_maxwell import params\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import wave_equation as w1d\n", + "from dg_maxwell import utils\n", + "\n", + "af.set_backend('opencl')\n", + "af.set_device(1)\n", + "af.info()\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Set the initial conditions\n", + "\n", + "E_00 = 1.\n", + "E_01 = 1.\n", + "\n", + "B_00 = 0.2\n", + "B_01 = 0.5\n", + "\n", + "E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + E_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + B_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2)\n", + "u_init[:, :, 0] = E_z_init\n", + "u_init[:, :, 1] = B_y_init" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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gY4zJAXIdx8nrw2GWAjnGmEpgG1AJJAHpgBvvvs2VvT14fHy8igoiIiIiIiISMsJ++oMx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\n0oVDL/+YSOPh45jLyZh1pe0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xREQ6VF52hCkNBQCMv/o+y2kkkNKu+jwA085voer0Cctp\nREQ6VvTuBqJNM4dcYxiXebntOEGjooKIXOCKiODASO8qtc5uFRVEJHSVvLsOl3EoipzMyDETbceR\nABo3dQ4lEROINs0UvvmM7TgiIh1y7fOuS1Y6arHlJMGlooKIXCR14QMATDv3IeeqKiynERFp36CS\nlwE4PeZGy0kkGE6OuwOA+KLnLScREWlf7flzTKneDMCweUstpwkuFRVE5CIZMxdy2HUZsaaRfW8+\nazuOiMglqs6UM7V2BwCjrwyfOavhbPynvFMgptbv4uSxA5bTiIhcat/7fybO1HOcYWTMvNJ2nKBS\nUUFELmJcLo6Nvg2AmH1/spxGRORS+99dT5Rp5qBrLGMmzbYdR4Jg1LhM9kVNw2Uc3G89ZTuOiMgl\nmgr+DMChEYswrvDqZofXqxWRbhl9jW9RrNrtVJw8ZjmNiMjFIgq9c1bL0pZYTiLBVDXxLgCSD7xg\nOYmIyMUa6uvIrHofgMSsz1hOE3wqKojIJcZMms3+iIlEGg/739KiWCISOmqqq5hSvQUIvzmr4W7i\ndZ+nyXExuamIo8Uf244jInJB4aaXSeA85SQxec4i23GCTkUFEWnX6QneRbES9mtRLBEJHYXvP88g\n00CpGUH6jAW240gQpYwYzZ5BVwBw5F1NgRCR0FGzy/t5uSTlU0RERlpOE3wqKohIuyZc9yAexzC1\nsYCyw/ttxxERAaC54C8AHB5+Q9jNWRWon+IdVpx25CUcj8dyGhERaG5qIuP02wDEzfq05TR26H9j\nEWnXiNEZ7I2ZAcDBt3VFSETsaz1nNWnOPZbTiA1Trv8c9U4U4zxHcBdssR1HRISi7RtJpZKzxJO5\n4FbbcaxQUUFEOlQ9yVttHXZQi2KJiH37PniRIabWN2f1BttxxIIhickUDPZOezn5gQreImJfVf4f\nAShMvIromFjLaexQUUFEOpR5vXdRrIxmN8cPFdqOIyJhrm53y5zV63BFRFhOI7Y4072jVEaXvWE5\niYiEO8fjYdyJjQBETr/Lchp7VFQQkQ4lpY6kKHoaAIc3acFGEbGnuamJiRW+Oauzw2+7LvnE5Kvu\nosGJYIxTypHi3bbjiEgYK9n9AaM4RY0Tw5SrVFQQEWlX1RjvEOPYA7mWk4hIOCvcmksyZ6kinikL\nbrYdRywakphMUexMAI5tUcFbROw5tWUDAPsGz2dQ/BDLaexRUUFEOjUy+04AMms/ovb8OctpRCRc\nnd3hnbNalHgNUdExltOIbdVjvQXv+EMbLScRkXCWdjwPAM+U2y0nsUtFBRHp1PgpcyhjGLGmkcJN\nL9mOIyJhyPF4GH/SO38+akb4Di+VT6TN9baDzLpdVJ89YzmNiISjQ/vyGec5QoMTweRrltqOY5WK\nCiLSKeNycSjlKgDq97xiOY2IhKPine8xknLfnNU7bceREDBm4iyOmlFEm2aKPnzRdhwRCUPHN3mn\nPuwdlEVCUorlNHapqCAiXYqdfhsA406/h+PxWE4jIuGmfKtvzuqQBcTGDbacRkKBcbk4OuwaAJr2\nqeAtIsGXcuQ1AOon3WY5iX0qKohIlzIX3EqtE81IyjmwZ6vtOCISRhyPh9HHvQvFeqbeYTmNhJL4\nGbcCkH7mfTzNzZbTiEg4OX6okEnNxTQ7hoyrl9mOY52KCiLSpdi4wRTFXQHAie1/tpxGRMLJ4cId\njHFKaXAiybz6HttxJIRMnncTNU4MqVRSsvsD23FEJIwcen8dAPtiZpAyYrTlNPapqCAi3VI3YTEA\nSUfftJxERMJJ6SbvB7e9cXMYkphsOY2EkpjYOArjswEoz3/BchoRCScJB14F4NyEWywnCQ0qKohI\nt4xbcDcAkxv2UlleZjmNiISLYUe9Ux8aNGdV2tGYcSMAKaUqeItIcJSXHWFKQwEA46++z3Ka0KCi\ngoh0y8ixkzjgGk+EcSj+UFMgRCTwSg/sY2JzCc2OYeI199qOIyEofaG34D2xcT/lZUcspxGRcFDy\n7jpcxqEocjIjx0y0HSckqKggIt1WNvJa7x+KXrMbRETCwuEP1gKwL2YWQ4eNspxGQlFq2jiKIzJw\nGQf3h8/bjiMiYWBQycsAnB5zo+UkoUNFBRHptqTZtwMw6dwmmhobLKcRkYEu8aB3zmp1uuasSsfK\nR10HQGTJ63aDiMiAV3WmnKm1OwAYfaVG0LVQUUFEum1S1vVUEU8i59mfr/mrIhI45aWHyGzYC8D4\nq/XBTTo29PKWgvdWGhvqLacRkYFs/7vriTLNHHSNZcyk2bbjhAwVFUSk2yKjotk/ZAEAlTtftJxG\nRAaykve8c1YLIzMZMTrDdhwJYZOu+BQVJDDE1FK4VaMVRCRwIgq9n3/L0pZYThJaVFQQkZ6ZfBMA\nI8vesRxERAayWLd37ZaKMfrgJp1zRURQknglANW7XrKcRkQGqrra82RWbwUgde5nLKcJLSoqiEiP\nTLry0zQ7hgmeg5Qd3m87jogMQHU11WTWfgTAyOw7LaeR/sCVeTMAaadU8BaRwNi/9XXiTD2nGErG\nzCttxwkpKiqISI8kphP3cyoAACAASURBVIygKHoqAIc2/clyGhEZiIo2v0qsaeQkyYyfOtd2HOkH\nJl15J41OBGM9xzjmLrAdR0QGoPMF3sWDDyQtxLjUjW5N74aI9Fjl6OsBiD2QZzmJiAxENXu8H9wO\nDr1SH9ykWxKSUiiKmQ7Akc3aWlJE/G/UqfcAiJisrSTb0v/UItJjI+bcBcDkmh3U1VRbTiMiA81l\n5e8DEDVFH9yk+86NXQRA3KGNlpOIyEBTerCQcZ6jNDkuJi68w3ackKOigoj02IRpcykjlUGmgcJN\nL9uOIyIDyDF3AWOcUhqdCCYu0Ac36b5Rcz8NwJTanZw/V2k5jYgMJEe2/BmA/dFTSRyaajlN6FFR\nQUR6zLhcHEq5GoC6Aq20LSL+c3TLXwAoipnGkMRky2mkPxk7aRbHzAiiTRNFH2rbYxHxn5iDbwBQ\nddl1VnOEKhUVRKRXYqbdAsC40+/jeDyW04jIQBF7yPvB7axv7RaR7jIuF0dTrwGgce8rltOIyEBR\nX1fD5PP5AKRecZvlNKFJRQUR6ZXMBbdR50QxklMc3LfddhwRGQDqas8zuca7leSIrNstp5H+aND0\nWwEYf+YDFbxFxC+KtuQSZ+opJ4mMmQttxwlJKiqISK8Mih9C4aDLASjb9hfLaURkICja/CqDTAMn\nSWbCNG0lKT03ef7N1DgxDKeCkt0f2o4jIgPA+QLvyCdtJdkxvSsi0mt1ExYDkHjkDctJRGQg+GQr\nSX1wk96JHRRPYfwcAE7lq+AtIn3XspWka/ISy0lCl/7HFpFeGzP/bgAyGwqoOn3CchoR6e8u831w\ni8zUVpLSe43p3g/+ycfetJxERPq744cKGec5QrNjmLjgTttxQpaKCiLSa2njMznoGkuEcdj/4Z9t\nxxGRfuyYe6+2khS/GL/QW/Ce1FhExcljltOISH92eLNvR6LoqSQmD7OcJnSpqCAifXJ8xLXePxS9\nZjeIiPRrR7f69gCP+f/s3WlzlFe67vn/Ss3zDEIgEMoUGDMYhMTgeQDbuLznqjpx+m2frjof4ETV\n3v0ButrV51VHR/SuOi87TkTXcHrv2rvKE2BjPAGSAGMwBmWmJhASaJ7HXP3iybQpikFDSiuH6xdB\nmALxcIWHYunSs+77aYpLKxynkWS2YfN2ghl+fMYS+uJfXccRkSSWHV0lObL5JcdJEptKBRFZlZJ9\n3oR2/9h5FhcWHKcRkWSV+90OcB3cZPXubfL+PfIFP3ScRESS1ezMFDsnvQ1nVQe0kehxVCqIyKrs\naHqNMQooY5z2i7q/KiLL562SvATAhkZdfZDVK9vvfQLQMHGB+blZx2lEJBm1t3y/SrJ+j1ZJPo5K\nBRFZlcysbNqLDgMwfPnfHacRkWTUfuGD71ZJ1u8+5DqOpICG/S8xTDHFTHGz5ZTrOCKShCauRldJ\nlhzBl5HhOE1iU6kgIqtmG7xJ7Rv7PnGcRESS0eS16CrJ0iNaJSlxkZGZSbDkCADjX//JcRoRSUbV\nWiW5ZPqTW0RWzX/0b4lYQ32kk76eoOs4IpJkaga0SlLiz7fzTQA23T3rOImIJJu+7nbqvlslqWt5\nT6JSQURWraxqEzezngKg65wmbYvI0vV2fMvWyG0WrA+/Dm4SR4Gjf8OC9bEt0kNvx7eu44hIEuk6\nH91IlL2LkoqNjtMkPpUKIhIXw1teBiCnQ3dXRWTpei54B7eb2U9TUlbpOI2kkpKySm7k7Aag5/y/\nOE4jIskku+M0AMM1LzpOkhxUKohIXGw4+LcA7JxsY2ZqwnEaEUkWObFVklu0SlLib7z2VQDyOlV4\ni8jSzM3OsGPyIgCVWiW5JCoVRCQu6ncfop8K8swcN86/5zqOiCSBP1slqYObrIFNTX8DwM7pr5ia\nGHWcRkSSwc2WDykwMwxSgn/vs67jJAWVCiISF8bno7P8OQBmrr3rOI2IJIP2lg/JN7Pco4z6PUdc\nx5EUtHXnAXrNRnLMPDe/1BYIEXmyiaveRqKwVkkumUoFEYmbnF0nAKgd/AwbiThOIyKJbvLaBwB0\nlB7VKklZE8bno6fieQBmr+stOhF5so13vY1ERqskl0x/gotI3Ow4+gNmbRY19i7dNy65jiMiCW5T\ndAd4xg6tkpS1k7f7LQC2D6nwFpHH6+sJsj3SxaI1NBz5a9dxkoZKBRGJm/zCEm7k7QfgTotWS4rI\no93pusG2SA8L1kfgqFZJytrZceQEUzaHDQwRvnrOdRwRSWDd5/8NgPasp7RKchlUKohIXE3XvQZA\n8a2PHScRkUT23cEte5dWScqays0r4GZBIwB3L/6b4zQiksiyYqskN2sj0XKoVBCRuKo9/HcA7Ji9\nxujQPcdpRCRRZcdWSW5+2W0QSQuz27270WW3zrgNIiIJa252hoaJNgAq9//AcZrkolJBROKqZvtT\ndPlqyTQRgl/+wXUcEUlAszNT7JyMHtwO6OAma6/u6N8CsGP+W4bv3XGcRkQSUXvraQrNtLdKct9z\nruMkFZUKIhJ3dza8CIC98b7jJCKSiNpbTpJvZhmgFP/eo67jSBrYuMVPKGM7PmMJfvEvruOISAIa\nu+qtRA+XHNYqyWVSqRBnxph6Y0yj6xwiLhXt9b7y6B87x+LCguM0IpJoJq56q/20SlLW091q7460\nL/ih4yQikoiq+6OrJBu0SnK50v5PcmNMqTHmnei3nxljfmWM+ckqHvlDoM0YM2yMOWmM+V30r6Ho\nX0vjlV0kUe1oPsYY+ZQxTvulM67jiEiCqY6ukvRpB7iso7Jn3gagYfwCC/NzjtOISCLpvxVie6ST\nRWsIaJXksqV1qRD9BL8N+I219ufW2l9aa38K+I0xv1rFo08BQ8Cx6Ldy4B1r7XFr7ciqg4skuKzs\nHNoLDwEwfPmPjtOISCLp626nLtKjg5usu4bGVximiGImudl62nUcEUkgXdGNRMGsnZRWVjtOk3zS\nulQAfgf83lp78f4ftNb+HPixMebYCp/7U2ut31prrLVl1tqD1tpfrzqtSBKJBF4HYEPfJ46TiEgi\n6TrvDXC9mb2LkvIqx2kknWRkZhIqPgLA6BUV3iLyvcywVzQO1WiV5EqkbalgjKnHe4vgUW8k/BZ4\nZ/0SiaQW/7N/S8Qa/Ith+m+FXMcRkQSRHd0BPqId4OLCzjcA2NSvwltEPPNzszRMtAJQoVWSK5K2\npQLe7AOsteFH/HwIaNQMBJGVKd+wmfasHQB0fvmvjtOISCKYm51hx6T3cmDVgbcdp5F01HD0b1mw\nPuoiPfR23nAdR0QSwM3W0xSZaYYoJvDM867jJKV0LhWOA4+bbxArG5rWIYtIShra/AoA2R2nHCcR\nkURws+VDCswMA5RSv0erJGX9lZRXcTP7aQB6zmu1pIjA2NfeRqJwsVZJrlSm6wAOleMNU3yUWOFQ\nv5KHG2N++OCvtdb+ciXPihkbG2NxcfGJH5eTk0NOTs5qfiuRuKhq/Gvo+md2TrYxMz1Jbl6B60gi\n4tDE1fcB6Cg5QqUObuLIWO2rEL5Kbscp4B9dxxERxzb2n/W+o1WSK5bObyo86VpDrHBYyfWHnwKn\notskfhkrE4wxJ1fwrO/U1NRQUlLyxG+/+MUvVvPbiMSNf+9R7lJOvpnl5vn3XccREceq734KaJWk\nuFXd/DcAPDV9mamJUcdpRMSlu7c7qI90enPAtJFoxdL9TYVHzVO4X8Uyn/v7h81psNb+0hjzT8aY\nn630jYXe3l4KCp78lV69pSCJwvh8dJY9y4bhPzJ99U/w8j+4jiQijvT1BKmLdEdXSf6V6ziSxrbt\nbOQOVWwy97h87l32H/uPriOJiCOd5/7ABqA9awc7qza5jpO09KZCnD1m8CPAKVaxUaK4uHhJ31Qq\nSCLJ2nUCgNrBz7CRiOM0IuJK1zlvlWR79i5KKjY6TiPpzPh8dFe+AMDs9fccpxERl7RKMj7SuVQY\nYWnFwmAcf88wgDGmMY7PFEloO46+zZzNpMb2033zsus4IuJIbJXkcM2LjpOIQO7utwCoU+Etkra8\nVZItgFZJrlY6lwqPG9II3vUIePyGiOUKRf+qjRKSNgqKSvk27xkA7rT+wXEaEXHBWyXZBkClVklK\nAth5+ATTNpuNDNLxTYvrOCLiQHvbRxSZaYYpJvDMC67jJLV0LhUu8vjNDrG3GJYydwEAY8yvjDGh\nJ3/kEwsNkZQyte01AAp7zrgNIiJO3Gw9SYGZYZAS/HufdR1HhNz8Qm7key+O9l/8o+M0IuLC6Nfv\nAhAqPqRVkquUzqXCkzYx1ANYa08t45lNQLkx5lHXKmI/fnEZzxRJepsavVfKdsxcZXpy3HEaEVlv\nE7Ed4CVHdHCThDGz1btDXXT7rOMkIuLChn5vIxEBbSRarXQuFU7BY+cbNMc+ZjnPtNaWWWsfdWXi\nPwAjTxjmKJJytjbso58Kss0CwdZVbVYVkSS08e5nABitkpQEsqnRm6vQMHONmakJx2lEZD3d6+3E\nv9jhrZI8+jeu4yS9tC0Vop/YnwJ++ogP+SEP2dRgjCk1xrxjjDn2kF/zG2PMzx72MGNMPdAI/GiF\nkUWSlvH56C49BMDk9eV2dSKSzPp6gmyPdLFoDQ3aAS4JZGvDPu5STo6Zp12Ft0ha6YxuJApmNVCm\nVZKrlralQtSPgGMPvq1gjPkd8OtHXH34CfAzHnJ9wlp7Mfrr/6xYiBYKJ4GfL/M6hUjKMP5XAKi6\n96XjJCKynrrP/xsA7VlPaZWkJBTj89FVehiACRXeImklI+z9Nz+4Sask4yHTdQCXrLUjxpiDwDvG\nmBG89ZF+4KS19teP+GWn8DZC/PYRz/ylMeaYMeZXeBskSqMf/6NY6SCSjuqa34K2n+FfDDPYf4uK\njVtcRxKRdZAVWyW5WQc3STzG/wq0vUfVXRXeIuliYX6OwEQrAOXPvOU4TWpI61IBvGKBR1+BeNjH\nXwTKnvAxp1j+PAaRlFZZXUvYV0d9pJOOlnepePsnriOJyBqbm52hYaINDFRqB7gkoFjhHVgMMXT3\nNuUbNruOJCJr7GbbRzzNFMMUEdj/ous4KSHdrz+IyDq6W3UUgEjwY8dJRGQ9tLeeptBMe6sk9z3n\nOo7IX4gV3gAdLe+5DSMi62L0SmyV5GEyMtP+a+xxoVJBRNZN/lPefNOtIxewkYjjNCKy1sauege3\ncMlhrZKUhBUrvBeDHzlOIiLr4ftVkg+buy8roVJBRNZNw6E3mLOZVDPArdDXruOIyBqr7o+ukmzQ\nKklJXN8V3sMqvEVS3UBvF/7FMBFrqNdGorhRqSAi6yavoIj2nN0A9F7Ua6Yiqaz/VojtkU4WrSGg\ng5sksEDz8WjhfY9b4Wuu44jIGgqf/36VpGaoxI9KBRFZV+M1zwOQ3fWJ4yQispa6oqskg1k7Ka2s\ndpxG5NHyC0toz3kagN62dx2nEZG1lBmKrZLUgMZ4UqkgIuuqfN8bAAQmL7EwP+c4jYislcywdz99\nqEarJCXxjde8AEB291nHSURkrdy/SrJMqyTjSqWCiKwr/77nGKWAIjNN8LIObyKpaHFhgcBkGwDl\n+950nEbkycr3vQ6Af/KiCm+RFBX66jOKmWSUAhr2q/COJ5UKIrKuMjIzCRUcBGD46knHaURkLYSu\nfE4xk4yRrx3gkhT8+55nlAKKmSL01Weu44jIGhi6+iEAoYJGrZKMM5UKIrLu5uu8drikVwc3kVQ0\n+PUHAITyD+jgJknh/sJ7KPrvr4ikluLezwGY36ayO95UKojIutty8AcANMxdZ2Js2HEaEYm3oujB\nbU4HN0kisU80Su587jiJiMTb1MQoDbPfAFDTeMJxmtSjUkFE1t3m+l30mo1kmUVCrfqKkEgqmZma\noGHGW8u36YDmKUjy2NLkDW4LzH7D5PiI4zQiEk/B1lNkmwX6qGJL/W7XcVKOSgURcaKn7DAA09+e\ndpxEROKpvfU0OWaefiqoDexzHUdkyTbX76bXbCTbLBJs+dB1HBGJo6noebO7tBnj06fA8aa/oyLi\nRGbgVQCqB845TiIi8TRx3dsB3l16SAc3STq3yg4BMH1DhbdIKqm85503fYFXHCdJTfrTXkSc8B86\nQcQa6iLd3OvtdB1HROKk8u4XAJh6reuS5JMReA2Ajfe+dJxEROJl+N4dAoshAOqaNE9hLahUEBEn\nSiurCWUFAOi88CfHaUQkHkYG+vAvxA5ubzlOI7J8scJ7e6SLgd4u13FEJA7CLe8C0OGro7K61nGa\n1KRSQUScGdhw1PtOxxmnOUQkPsIt7+Ezlk7fViprtrmOI7JspZXVhDL9AHS2vus4jYjEw2LwYwD6\nq444TpK6VCqIiDNFTx8HoG60BRuJOE4jIqs1Hz249VXq4CbJa2DjswDY0MeOk4hIPGwZvgBA3s7X\nHCdJXSoVRMSZwMHXmLbZVDFM57dtruOIyCptHvIObrk6uEkSK9p1DIC60QsqvEWS3O3wdWpsP/M2\ng0Dz667jpCyVCiLiTG5eAe15ewHov/y+4zQishq9nTfYYu+wYH0Emt9wHUdkxQJNx5ixWVQxTPeN\nS67jiMgq3L74HgDt2bsoKCp1nCZ1qVQQEaemtrwAQF7PWcdJRGQ1brV5B7dg9lMUFpc5TiOycrl5\nBbTneoX3nUvvOU4jIquR0fkJAKObnnWcJLWpVBARp6r2eV/RbJj6irnZGcdpRGSlYge34Wod3CT5\nTUYL79yeTx0nEZGViiwuUj/hXa8t233ccZrUplJBRJzavvswQxSTb2YJXtRQLJFkFFlcZPt4KwAl\nOrhJCqh65k0AGqYuMz836ziNiKxE+Oo5yhhn0ubiP/CS6zgpTaWCiDjly8ggXNQMwOi1Dx2nEZGV\n6PimhXLGmLI5BA687DqOyKrFCu8CM0O7Cm+RpDRw5QMA2vP3k5Wd4zhNalOpICLO2e1ee1ze94Xj\nJCKyEve+O7g9Q3ZOruM0Iqvny8igo6gJgNFrJx2nEZGVyL/9OQAztS84TpL6VCqIiHO1zT8AIDB/\ng9HhAcdpRGS58qL3zqe36OAmqSOy/WUAyu587jaIiCzb7MwUDdNXAKg+8KbjNKlPpYKIOFddG6Db\nt5kMYwm3aLWkSDKZm5357uC24RmtkpTUUdv0FuAV3mMjg47TiMhyBNs+Js/MMUAp23Y2uo6T8lQq\niEhCuFN+GIC5m6cdJxGR5Qhe/Jh8M8sgJdTtanIdRyRuqrc20GNqyDQRQhe0WlIkmYx9411b6ixu\nwvj0Ke9a099hEUkI2TteA6Bm8JzjJCKyHGPR++YdRU34MjIcpxGJr96KI4AKb5FkU97vzemKXWOS\ntaVSQUQSgv/QCRasj1rby52uG67jiMgSlUYHrMYGroqkkljhvWnovOMkIrJUo8MDBOZvArC16YTj\nNOlBpYKIJITi0gqCWTsB6GnVa6YiyWB8dIjAvFcCxu6fi6QS/6ETLFrD1sht+nqCruOIyBKEW94n\nw1i6fZuprg24jpMWVCqISMIY3vQcABmdnzhOIiJLEWr5gEwTocfUUL21wXUckbi7v/Dubn3XcRoR\nWYq5mx8B38/rkrWnUkFEEkbJ7uMA1I+3EllcdJxGRJ5k5oZ3z7y3/JDjJCJrZ7jaK7x94TNug4jI\nklRHrytlNbzqOEn6UKkgIgmjofEVJm0uZYwRvqqBjSKJrjo6WDWr4RXHSUTWTvF3hXeLCm+RBNd/\nK8S2yC0WrcHf/KbrOGlDpYKIJIys7Bza8/cDMHDlA8dpRORx7vV2UhfpIWIN/mYNwpLUFWh8hSmb\nQzljdHzT4jqOiDxGd3QuVyirgZLyKsdp0odKBRFJKDO1LwBQcOtTx0lE5HE6W7z75aGsACUVGx2n\nEVk72Tm53xXe977SIGGRRGai15QGNz7rNkiaUakgIgll0wHvK54NM18zMz3pOI2IPFL04Daw4ajb\nHCLrYDpaeOff+sxxEhF5FBuJUDfmvU1U9PQxx2nSi0oFEUkoW3ce4C7l5Jp5gq2nXMcRkYewkQjb\nRqMHt106uEnqq44V3tNXVHiLJKjuG5eoZIRpm02gUUMa15NKBRFJKMbno6ukGYDxb1QqiCSi7vYr\nbGCIWZtF4OBrruOIrLltOxu5Rxl5Zo5g22nXcUTkIe5cfh+AYO4ecvMKHKdJLyoVRCThGL83Sb7y\n7heOk4jIw/Rd8u6Vt+fuJje/0HEakbVnfD46VXiLJLTcHm8e1+Tm5x0nST8qFUQk4dQ1vQWAfyHE\nyECf4zQi8qDs7rMAjNfo4CZppF6Ft0iimp+bJTB5GYDKZ95wnCb9qFQQkYRTWbONDt82fMYSuvAn\n13FE5D4L83MEJi8BULlPBzdJH3XN0cJ7PqjCWyTBhC6fpdBMM0Ih9Xs0QHi9qVQQkYTUX+X9gbAY\n/NhxEhG5X/CrTyky04xSQP1ereyS9FFVU0enbys+Ywm3aLWkSCIZvnoSgHDhQXwZGY7TpB+VCiKS\nkPJ2esPftgyfx0YijtOISEzs4BYqOEhGZqbjNCLrq6/SK7zn2z9ynERE7lfS511Lmt/2kuMk6Uml\ngogkpIZDbzBnM6ixd+ntvO46johEFfd+DsD8thccJxFZf3lPeWvqtgyfd5xERGImx0cIzH4DwJaD\nbzpOk55UKohIQsovLKE952kAbrW+6ziNiABMTYzSED241TSecJxGZP0Fmt9k3maw2fZzO6zCWyQR\nBFtPkm0W6TUbqKnb5TpOWlKpICIJa2zTcwBkdX3iOImIAARbT5FtFuijii31u13HEVl3BUWltGd7\nn7TcatMgYZFEMP3taQBulR7C+PTprQv6uy4iCat8rzdZPjB5kcWFBcdpRGQqenDrLm3WwU3S1mh0\nlaoKb5HEsOHelwBkBF5xnCR96UQgIgkrsP9FxsinmElCVz5zHUck7VVFD24+HdwkjZXtfR0A/0Sb\nCm8Rxwb7b1Ef6QRge7Ou5bmiUkFEElZGZiahgkYAhq586DiNSHobvncH/2IYgLomHdwkfQWeeYEx\n8ilhkvDXX7iOI5LWOlq99a6hjHrKN2x2nCZ9qVQQkYQ2F10NVNT7qeMkIukt3OINTO3w1VFZXes4\njYg7mVnZhPIPADBw5X3HaUTSWyT4MQD3Kg87TpLeVCqISEKLTZhvmL3G1MSo4zQi6WsxenDrrzri\nOImIe7HCu/i2ruaJuGIjEbYOXwAg/6ljjtOkN5UKIpLQttTv5g5VZJtFgi0nXccRSVtboge3vJ2v\nOU4i4l5N45uAV3hPT447TiOSnm6Hv6Gae8zZDALNx13HSWsqFUQkoRmfj54y75W2qW9POU4jkp5u\nh69TY/uZtxkEml93HUfEuS3+vfRRRbZZoL1FM39EXLh90Zun0J7zNPmFJY7TpDeVCiKS8GIrgjZG\nJ8+LyPq61ebNU2jP3kVBUanjNCLuGZ+P7tJmAKau6y06EReyus4CMLbpOcdJRKWCiCS8+kM/AGB7\npJPB/luO04ikn6yuTwAY3fSs4yQiiSO2WrVy4ILjJCLpZ3FhAf9kGwBle3T1wTWVCiKS8MqqNhHK\n2A5AZ6smbYusp8jiItsnLgJQtlsHN5GY2GrV+oUwIwN9jtOIpJfw1S8pYZIJm0dg/4uu46Q9lQoi\nkhTuVXoT5xdDZ9wGEUkz4avnKGOcSZuL/8BLruOIJIzK6lo6fNvwGUu45T3XcUTSysAVb5ZJe8EB\nMrOyHacRlQoikhTydr4KwOZhvWYqsp4GrnwAQHv+frKycxynEUks/ZXeIOH54Bm3QUTSTOHtTwGY\nrX3BcRIBlQoikiT8TceZtxlstv30dt5wHUckbeTf/gyAGR3cRP5C7g6v8K4ZUuEtsl5mpibYMXMV\ngE0H3nScRkClgogkicLiMkLZOwG41abXTEXWw8z0JA3TXwNQrYObyF+ob3qdRWuotb309QRdxxFJ\nC8G20+SYee5SztYd+13HEVQqiEgSGdl4FABf51nHSUTSQ/DiR+SZOQYoZdvORtdxRBJOcWkFwawd\nAHS3qvAWWQ/j108B0FXShPHp09lEoH8KIpI0ip4+BkDdeBs2EnGcRiT1jX9zGoDOYh3cRB5lKFZ4\nd3ziOIlIeqi4e877zvaXneaQ7+mEICJJI9D4MtM2m0pG6Py2zXUckZRX3v8FABEd3EQeqWjXawBs\nG2tV4S2yxkaH7hGYbwdgW/NbjtNIjEoFEUkaObn5tOftBaD/8geO04ikttHhAQLzNwHY2nTCcRqR\nxBU4+BozNosqhum+edl1HJGUFm55F5+xdPlq2bB5u+s4EqVSQUSSylTNcwDk3vrMcRKR1BZueZ8M\nY+n2baa6NuA6jkjCys0rIJi7G4A+Fd4ia2ru5kcA9FUcdpxE7qdSQUSSSsW+1wHwT15mYX7OcRqR\n1DV305uncKdcBzeRJxmPFt7ZPSq8RdZSbH1rzo7XHCeR+6lUEJGkUr/nKKMUUGSmCX2lw5vIWtk0\ndB6ArIZXHScRSXwVe2OF9yUWFxYcpxFJTX3d7dTaXhatob75Dddx5D4qFUQkqWRkZhIq8FbbDV89\n5TiNSGrqvxVia+Q2i9bgb37TdRyRhFe/91nGyKeYScJff+E6jkhK6m7z1rYGs3ZSXFrhOI3cT6WC\niCSd+a3PA1B453PHSURSU3erd3ALZTVQUl7lOI1I4svMyiaUvx+Aga9POk4jkppia1uHqp91nEQe\npFJBRJJO9X7vK6cNM9eYmZpwnEYk9ZjwGQAGN+rgJrJUs7XRwvu2ruaJxJuNRNg+1gJA8dPHHaeR\nB6lUEJGks7VhH3cpJ8fME2w77TqOSEqxkQh10YNb0dPHHKcRSR7V+7073oGZq8zOTDlOI5JaOq+3\nUMEoUzaHQOPLruPIA1QqiEjSMT4fXSVNAIxfV6kgEk9dNy5SyQjTNptAo4Y0iizVtp2NDFBKnpkj\n2Pax6zgiKaU/uq41mLePnNx8x2nkQZnxepAxpthaOxav560XY0wp8E/R/zkI+IE2a+2vE+mZIvKA\n7S/B5Q+puPulwqZG6AAAIABJREFU6yQiKaXv0vvUAcHcPezNK3AdRyRpGJ+PzuImKsdOMXb9FDz3\nA9eRRFJG3q1PAZja8pzjJPIw8XxTodMYs2iMed8Y81+MMfvj+Ow1Ef3kvw34jbX259baX1prfwr4\njTG/SpRnishf2tp0AgD/fDujwwOO04ikjtxb3n3wic3PO04iknxs3YsAlPWp8BaJl/m5WQJTVwCo\njK5vlcQSz1LhJ8Bl4HXgl0BbEpQMvwN+b629eP8PWmt/DvzYGLOSy6Rr8UwRecDGLX56TA0ZxhJu\ned91HJGUsDA/R2DyMgCV+3RwE1muLQe9QcKB+RuMjw45TiOSGkKXPqHAzDBMMfV7jriOIw8Rt1LB\nWvt7a+1Ba60Pr1j4r/xlyTBojPmNMeZ/jtfvu1LGmHrgGPCotwd+C7zj+pki8mi95YcAmGvX3VWR\neAhePkuhmWaUAur3HHUdRyTpbNq2k1ummkwTIdT6oes4Iilh+Jq3prWj8AC+jAzHaeRh1mRQo7X2\nVPTV/1jJcByvZDDAD4H/Fn2L4X9bi99/iX4YzRp+xM+HgMbodQaXzxSRR8hqeAWAjYMXHCcRSQ3D\nV72DW6jgIBmZcRu7JJJWbpd5hffMTRXeIvFQcucLAOa3veQ4iTzKumx/sNaejpYM5cD/AH4K/H/A\nP0avRxSvR44HHAdGHvPzsWKgyfEzReQR6pveJGINdZFuBvq6XccRSXrF3x3cXnCcRCR5Zfq9T3w2\n3DvnOIlI8pscHyEwdx34/nqRJJ51Xylprf0xUG+t/REQADLwrgWst3LgcZfdYuVAveNnfmdsbGxJ\n32ZnZ1fyeJGkU1pZTTjT+8+ps+U9x2lEktv05DgNs98AUHPgDcdpRJLX9mZvkHB9pJPB/luO04gk\nt2DrSbLNIneooqZul+s48ghxLRWMMX9vjPlPS33zwFobttYeB8aMMX8fzyxL8KQrCLFyYDlXFdbi\nmd+pqamhpKTkid9+8YtfrOTxIklpoMob2BMJnXEbRCTJeQe3BfqpYIt/r+s4IkmrfMNmwr46ADpb\nNUhYZDWmvz0NQE9pM8a37l8PlyWK24VJY8w/422AAPiVMaYNb2Dh76y1Yw98+J99pd5a+2NjzP+N\ndyVivZTz/XWEx6lw/Mzv9Pb2UlDw5J3hOTk5K3m8SFLK3/kq9P13akdasJGI/sARWaGJ6MGtu/QQ\nG/Xfkciq3K06Qn1/J4uhM8B/ch1HJGlVDZwHwBd4xXESeZx4TmEqB/zRbz8F/gFvdsCvjTFh4CLe\nV+qbePgn3qNxzLIUazEscU0HMBYXFy+pVBBJJ4Hm48ydyWCTucftzutsrt/tOpJIUqq8693/NvUa\nhCWyWnk7X4H+/5fNwxokLLJSw/fu4F/0Pm2sazrhOI08Tjy/FDFkre2Ibn74UXTrw4/x3j7wAz/C\nKxuGgf8FwBjzX4wxfxf99SVxzLIUIyytBBh0/EwReYz8whKC2d4du1ttes1UZCVGB/vxL4QA2KaD\nm8iq+ZveYN5msNn209t5w3UckaQUbnkXgA7fNiqrax2nkceJZ6nwK2PMn13mt9b+/r6Cocxa67PW\nvn7fdYj/Ffh9dJ7Cer+p8LiBiuC9eQGP3+awHs8UkScY3fQsAJldZx0nEUlOoZb38BlLp6+Wqpo6\n13FEkl5hcRmh7J0A3GrTIGGRlVgIngGgv/KI2yDyRHErFay1l/CuOvyzMeYXDw5rtNY+rDT4MfDf\n8LZB/GO8sizRRR6/hSH2xsFSZiSs5TNF5AlKdx8DoH7iIpHFRcdpRJLPfPvHAPRXHHacRCR1jGw8\nCoCvU4W3yErErg/l7nzVcRJ5krhOYopef/jPwP/+kOGMD/v4U9ba/2yt/a/xzLFEJ5/w8/XgZXT8\nTBF5Av/+l5iyOZQxRsc3La7jiCSdmiHv4JbdoEFYIvFS9LRXeNeNt2EjEcdpRJJLb+cNttg+FqwP\nf9PrruPIE6zJeOdHvJWQaE4BGGMaH/HzzbGPcfxMEXmC7Jxc2vP2AXDvyoeO04gkl76eILW2l0Vr\nqG9+03UckZQRaHyZaZtNJSN03bjoOo5IUoldGwpm7aSopPwJHy2upe3OKGttGO8T/J8+4kN+CLzz\n4A8aY0qNMe8YY47F65kisnrTW54DIO/WZ46TiCSX7tbYwW0HJWWVjtOIpI6c3HyCuXsA6Lv8geM0\nIskldm1opPpZx0lkKdK2VIj6EXDswTcLjDG/A379iGsKPwF+xqOvOqzkmSKySpV7vVfjAlNfMT83\n6ziNSPLwdXwCwFD0/reIxM/E5ucByOlR4S2yVDYSYft4K/D9NSJJbJmuA7hkrR0xxhwE3jHGjOCt\nevQDJ621v37ELzuFt73ht3F8poisUv2eIwz/SxFlZpxvL5/lqUPHXUcSSXg2EqFuzJtDUrTrNcdp\nRFJP5d7jEP4/CUxeYmF+jsysbNeRRBJe5/UWtjPKtM0m0Piy6ziyBGldKoBXAvDo6woP+/iLQFk8\nnykiq+fLyKCj8ABlE2cZvnYKVCqIPFH3jUtsY4QZm0XgoEoFkXir3/ssY38ooNhMcuOrz9jZpCn2\nIk/S/9WHbAfa8/ayLzffdRxZgnS//iAiKWR+64sAFN/53HESkeRwJ3rPuz13D7l5BY7TiKSejMxM\nQgUHABi+qhuwIkuRG70uNBW9PiSJT6WCiKSMmkZvcn3D7HWmJ8cdpxFJfDk9nwIwUfOc4yQiqWtu\n6wsAFKrwFnmi+blZAlNfAVC5T6skk4VKBRFJGVvqd9NHJdlmgWDro2apigjAwvwcgclLAFTs1cFN\nZK1U748W3jPXmJmacJxGJLGFLp+l0EwzQiH1ezRAOFmoVBCRlGF8PnpKmwGY+Pa04zQiiS301WcU\nmWnGKMC/T28qiKyVrQ37uEs5OWaeYJv+bBJ5nOFr3jWhcGEjvowMx2lkqVQqiEhKMfUvAVB595zj\nJCKJLXa/O1RwgIzMtJ/bLLJmjM9HV0kTAOPXVSqIPE5sLlZsTpYkB5UKIpJStjWdAMC/EGJ0sN9x\nGpHEFbvfHbvvLSJrx9Z5nyBV3P3ScRKRxDU1MUrD7HXg+zlZkhxUKohISqmqqaPLtwWfsYRaP3Qd\nRyQhzUxN0DBzDfj+vreIrJ2tscJ7vp2xkUHHaUQSU7D1FNlmgT4q2VK/23UcWQaVCiKScvrKDwEw\n3/6R4yQiiam99TQ5Zp67lLO1YZ/rOCIpr7o2QI+pIcNYwi0fuI4jkpCmovOwuksPYXz6NDWZ6J+W\niKScrIZXAageuuA4iUhimvjWm6fQVdKsg5vIOumNFt4zN1V4izxM5T1vHpYvOh9LkodOEiKScvzN\nb7JoDdsit7h7u8N1HJGEUxm7171dBzeR9ZLV8AoA1YMaJCzyoJGBPuoXwgDURa8LSfJQqSAiKaek\nvIpQVgMAXS3vOk4jklhGh+7hnw8CsK35LcdpRNKHv/kEEWuoi/Qw0NvlOo5IQgm3vIfPWDp9W6ms\n2eY6jiyTSgURSUmDG4543+n4xG0QkQQTankfn7F0+bawYfN213FE0kZJxUbCmfUAdLa+5ziNSGKZ\nD54BoK/isNsgsiIqFUQkJRU+dQyAbaMt2EjEcRqRxBEbYBobaCoi62egyiu8bfiM2yAiCaYmOgcr\nd8erjpPISqhUEJGU1ND0GrM2iw0M0d1+xXUckYSxaeg88P1AUxFZPwW7vMK7dkSFt0hMX3c7tbaX\nRWuob37DdRxZAZUKIpKScvMLac/1dhz3XX7fcRqRxHD3dgdbI7dZtAZ/85uu44iknUDTceZsJtUM\ncCt8zXUckYTQ3eZdBwpm7aS4tMJxGlkJlQoikrImNj0HQHb3p46TiCSG2ODSUFYDJeVVjtOIpJ+8\ngiLac3YB0HtRhbcIgC86/2po41HHSWSlVCqISMoq2+O9ZuqfvMTiwoLjNCIJIHpw+26QqYisu7Fo\n4Z3VddZxEhH3bCRC3VgrAEVPv+Y4jayUSgURSVn+Z55njHyKmSR05XPXcUScspEI20ZbACiK3usW\nkfVXtuc4APWTF4ksLjpOI+JW142LVDLCtM0m0KhZP8lKpYKIpKzMrGxC+fsBGPz6Q8dpRNzqbr/C\nBoaYtVkEDuqrQSKuBPa/yITNo5QJwle/dB1HxKm+yx8AEMzdQ25egeM0slIqFUQkpc3WvgBAUe9n\njpOIuBUbWNqeu5vc/ELHaUTSV2ZWNsH8ZwAY+OoDx2lE3Mrp8c5nE5ufd5xEVkOlgoiktE0HvAn3\ngZlrzExPOk4j4k529P52bICpiLgzEy2883t1NU/S18L8HIHJSwBU7j3uOI2shkoFEUlpW3fs5x5l\n5Jp5gm2nXccRcWJxYQH/1GUAyve97jiNiGzc/wYADdNfMzsz5TiNiBvBrz6lyEwzSgH1e591HUdW\nQaWCiKQ04/PRVdwEwPh1lQqSnkJXPqeYScbIx79Pr5iKuFb31EEGKCXPzBG8eMZ1HBEnhq+eBCBU\n0EhGZqbjNLIaKhVEJOVFtr8EQEX/F46TiLgRG1Qayt+vg5tIAjA+H51FBwEY++ak4zQibhT3euey\n+a0vOE4iq6VSQURS3tamEwD459sZHR5wnEZk/cUGlcYGl4qIezZaeJf1aQOEpJ/pyXEaZq8BsOnA\nG47TyGqpVBCRlFddG6DH1JBhLOGW913HEVlXM9OTBGZiB7c3HacRkZgtB6ODhOdvMD465DiNyPoK\ntp0i2yzQTwW1gX2u48gqqVQQkbTQW34IgLmbHzlOIrK+gm2nyTXz3KOMrTv2u44jIlGbtu3klqkm\n00QItWi1pKSXieveeay7pBnj06ekyU7/BEUkLWQ1vALAjoEPHScRWV+xAaVdxU06uIkkmNtlXuG9\ncOX3jpOIrK/Ke9FrP/UvuQ0icaHThYikBX/zCSLWUMY4d293uI4jsm5iA0pt/ctOc4jIX8oMvAzA\nlrGv3AYRWUejg/3454MA1DW/5TiNxINKBRFJCyUVGxk3+QB0tb7nOI3I+hgdHsA/3w58P7BURBLH\ntsbjAFRzj4G+bsdpRNZHuPV9fMbS5aulqqbOdRyJA5UKIpI2vqn5B+874TNOc4isl3DL+2QYS4+p\nYeMWv+s4IvKAyuqtBDO8/zY7L7zrOI3I+phrPwNAX3TelSQ/lQoikjaKdh0DoG70AjYScZxGZO3F\nBpP26uAmkrDubTgKgA197DiJyPqoGTwHQPaOVx0nkXhRqSAiaSPQdIwZm0UVw3TfuOQ6jsiaqx66\nAOjgJpLICqOF9zYV3pIG+m+FqLW9LFpDfbPWHKcKlQoikjZy8wpoz90DwJ3L7ztOI7K27vV2si3S\nQ8Qa6pt0cBNJVA1Nx5m1WWxgiO72K67jiKyp7uhcq1BWAyVllY7TSLyoVBCRtDK5+QUAcns+dZxE\nZG3FBpKGMv2UVGx0nEZEHiU3v5D23N0A9F3SIGFJcR2fADAYvfYjqUGlgoiklcpn3gAgMHmZ+blZ\nx2lE1o4NnQFgYMOzboOIyBON1zwPQHb3WcdJRNaOjUSoG20BoOjpY47TSDypVBCRtFK/5ygjFFJo\npgld1uFNUpONRNgaPbgV7tI8BZFEV7kvVnhfYmF+znEakbXRffMyVQwzY7MIHHzNdRyJI5UKIpJW\nfBkZhAsPAjB89aTjNCJr41boazYyyJzNJHBQXw0SSXT1e59llAKKzDTBr3Q9T1JT3+UPAAjm7iY3\nr8BxGoknlQoiknbmt70EQMmdzx0nEVkbvZe8g1t7ztPkFRQ5TiMiT5KRmUmoIFp4f/2h4zQiayO7\n2yvMxmuec5xE4k2lgoiknS0H3wKgYe46k+MjjtOIxF9Wl3e1Z0wHN5GkMb/tRQCKVXhLClqYn8M/\n5a3zrtj7huM0Em8qFUQk7Wyu38Vts5Ess0iwRaslJbUsLizgn7wIQNme447TiMhSbWmKFt6z36jw\nlpQT/voLiplijAL8+1R4pxqVCiKSlm6VHQZg+tuPHCcRia/w1S8pYZJxm0fgmRdcxxGRJaqp20Wv\n2UC2WSTYqpk/kloGo9d6Qvn7ycjMdJxG4k2lgoikpcyANxF/48A5x0lE4mvwSvTgVrCfzKxsx2lE\nZKmMz8et0kMATH972nEakfgq6vWu9cxtVdmdilQqiEhaqm9+k4g1bI90MdDX7TqOSNwU3PYGYc3U\n6uAmkmwyAq8AsOHel46TiMTP9OQ4DTPXAKg+cMJxGlkLKhVEJC2VVW0inFkPQOeFdx2nEYmP6clx\ndsxcBWBT4w8cpxGR5dre7H3CVR/pZKCvx3Eakfhob/mQHDNPH5VsbdjnOo6sAZUKIpK27m3wBgXZ\n8Bm3QUTiRAc3keRWvmEzwQw/AJ2t7zlOIxIfU9e9GSHdZYcxPn36mYr0T1VE0lbhrmMAbB25gI1E\nHKcRWT0d3ESS30DVEQAiwY8dJxGJj433vgAgo+E1x0lkrejEISJpq6HpNWZtFhsZpCd4xXUckVXT\nwU0k+RWo8JYUcq+3k+2RLiLW4D+ka3mpSqWCiKSt3PxC2nN3A3Dnol4zleSmg5tIagg0HWfOZlLN\nALdCX7uOI7IqnRf+CEAwq4HSymrHaWStqFQQkbQ2vvlFAHK6P3GcRGR1dHATSQ15BUXczN0DQG+b\nBglLcjNh7xrP4MbnHCeRtaRSQUTSWtUzbwLQMHmJudkZx2lEVk4HN5HUocJbUkFkcZH6sQsAlOx5\nw3EaWUsqFUQkrdXvOcIgJRSYGdrbPnIdR2RFIouL+GMHt71vOk4jIqu1Yb+3WlKFtySz8NVzlDPG\npM2l4eCrruPIGlKpICJpzZeRQUdxMwBjV993nEZkZcJXv6QsdnBrfMV1HBFZpe27D39feLeedh1H\nZEXufeWdq24WNJKVneM4jawllQoikvas35uUX9n/ueMkIitz77I3aFQHN5HU4BXehwAYu/aB4zQi\nK1N0+ywAc9tecpxE1ppKBRFJe9sPvw2AfyHE0N3bjtOILF/x7U8BHdxEUon1e6+LV/V/5jiJyPJN\nTYyyY+YqADUHtZEo1alUEJG0V1m9lVDGdnzGEr7wJ9dxRJZlamKUhlkd3ERSzfbDfwVAYFGFtySf\n9gsfkG0W6DUb2FK/23UcWWMqFUREgLsbvIn5tl13VyW5eAe3RR3cRFJMZXUtoYx6AMLn/+g4jcjy\nTH97EoCesiMYnz7lTHX6JywiAhQ9/ToAdaPnsZGI4zQiS6eDm0jqurvhWQBsUIW3JJdNA18CkLXj\nNcdJZD3o9CEiAjQ0H2faZlPFMJ3XW1zHEVkyHdxEUlfR7jcA2K7CW5JIX0+QbZEeFq3Bf0jX8tKB\nSgURESAnN5+bec8A0H/pXcdpRJZGBzeR1NbQdIwpm0MlI3R8o8JbkkNPizefKpi1k5LyKsdpZD2o\nVBARiZre+jIABT1n3QYRWSId3ERSW05uPu35XuF997IKb0kOvo6PARja9LzjJLJeVCqIiERtOuit\nltwx8zXTk+OO04g8mQ5uIqnv+8L7E7dBRJZgcWEB/7j3Vk3Znjccp5H1olJBRCRqa8M++qgkx8zT\nfuED13FEHksHN5H0sKnRu9q0Y+aqCm9JeOGvv6CUCcZtHv4DL7mOI+tEpYKISJTx+eguOwLAVHSi\nvkiiCl35XAc3kTTgFd5VKrwlKQx+9T4AwYJGsrJzHKeR9aJSQUTkPhkNxwCovve54yQijzd45T1A\nBzeRVOcV3ocBmLr+oeM0Io9X1OvNpZqre9ltEFlXKhVERO4TOPwWi9ZQF+mhryfoOo7II5X0fgbA\nXN0rjpOIyFrL3OEV3psGvnCcROTRJsaGaZj9BoAtTX/lOI2sJ5UKIiL3KanYSDBrB/D9ZH2RRPPn\nB7e3HacRkbXmP/w2i9awTYW3JLBgywdkm0VumWo21+9yHUfWkUoFEZEHDG16AQBf+CPHSUQeLnjh\nfbJ0cBNJGyXlVQSzdgLQfeGPjtOIPNxsdB7V7fIjjpPIelOpICLygLK9bwLgn2hlcWHBcRqRv6SD\nm0j6iRXeGdFVsiKJZtPglwBk7zzuOImsN5UKIiIPCBx4iTHyKWWC0JXPXMcR+Qs1OriJpJ2yvd7q\n2MBEiwpvSTh3um6wNXKbBevDf+iE6ziyzlQqiIg8IDMrm2DBQQAGv3rPcRqRP9fbeYNa26uDm0ia\niRXeJUwSvHzWdRyRP9PT+i4A7dlPUVxa4TiNrDeVCiIiDzEfXYVU2vup2yAiD7jV6g0Q1cFNJL3c\nX3gPff2B4zQify6zw5tDNRK9piPpRaWCiMhD1DZ7q5Aa5q4zNjLoOI3I9zI7vfvUOriJpJ/56ArZ\n0l69qSCJY3FhgcBEGwBl+95wnEZcUKkQJ8aYemNMo+scIhIfNXU76TE1ZJoIwfPvuo4jAujgJpLu\napu9FbINc9+q8JaEEbx8lmImGaOAwDMqvNNRWpcKxphSY8w70W8/M8b8yhjzkxU+7odAmzFm2Bhz\n0hjzu+hfQ9G/lsYzu4isvd6KowDM3zzlOImIRwc3kfSmwlsSUew6TrDgIJlZ2Y7TiAtpWypEP8lv\nA35jrf25tfaX1tqfAn5jzK9W+NhTwBBwLPqtHHjHWnvcWjsSl+Aism5ydr0OQO3Ql9hIxHEaERi6\n8j6gg5tIOuutfBaA+ZsnHScR8cTmT8XmUUn6SdtSAfgd8Htr7cX7f9Ba+3Pgx8aYYyt45k+ttX5r\nrbHWlllrD1prfx2XtCKy7hoOvcmczaDG9nM7/I3rOCKU3tHBTSTd5TzlrZJV4S2JYHx0iIa56wDU\nNv3AcRpxJS1LBWNMPd6bBI96I+G3wDvrl0hEElFBUSntObsBuN32R8dpJN2NjQzSMPctoIObSDr7\nvvC+y63wNddxJM0Fz79LponQY2qo2f6U6zjiSFqWCnjzD7DWhh/x8yGgMdHmIIyNjS3p2+zsrOuo\nIiljbPOLAOR0nXEbRNJe6MJ7OriJSLTw3gNAb6sKb3Fr7uZpAHorjjhOIi6la6lwHHjcjINY2dC0\nDlmWrKamhpKSkid++8UvfuE6qkjKqNp/AoCGyUvMzc44TiPpbO6Gd39aBzcRGdvsDWrN6f7EcRJJ\nd5sHvwQgZ+dxx0nEpUzXARwpxxuo+CixwqF+uQ82xvzwwV9nrf3lcp/zML29vRQUFDzx43JycuLx\n24kIUL/nKEP/Uky5GeNa20fsfvYt15EkTW0eOgdAzlOvO04iIq5V7X8LOv6v7wrv7Jxc15EkDd0O\nX2eLvcO8zSBw+ITrOOJQur6p8KRrDbHCYbnXH34KnIpukvhlrEwwxsRlPG9xcfGSvqlUEIkfX0YG\n4eJDAIxd+8BxGklXt8PX2GL7vIPboTddxxERx+r3HGGIYgrMDO1tH7mOI2nqVtufAGjPeZrC4jLH\nacSldC0Vynn89YeYimU88/fR1ZR/9txosdBkjPnZcgKKSOKw9a8CUNn3meMkkq5utXr76HVwExF4\noPC++r7jNJKusjrPADBa87zbIOJcupYKcR/A+JihjwCn0DYJkaS1/dDbAPgXQgzdve04jaSj7Oig\nUB3cRCTG+l8DoKpfhbesv4X5OQKTbQBU7NPVh3SX8DMVohsY6vHeLliJIWvtxQd+bISlFQuDK/w9\nHxQGMMY0PiSLiCS4yppthH111Ec6CV/4E+Vv/8R1JEkjC/NzBCbawOjgJiLf2374bbj0TwQWvcK7\nfMNm15EkjQQvn+UpphihEP++51zHEccSvlQAfoI3q2A1/A/878cNaYTvC4ylXJFYilD0r02ASgWR\nJHR3w3PU93Vi20/j/d+SyPoIXvqEp8y0Dm4i8mcqq7cSytiOf7GD8Pk/Uv5Xqz0uiyzd8NfenKlQ\nYRMHM5PhU0pZSwn/b0B0JkFctifc5yLww8f8fOwthsddafiOMeZXwDFr7YPlxYOeVGaISIIqePoN\n6Pvv1I2ex0YiGF+63h6T9TZy5T0AwoUHadTBTUTuc6/qWfx9HdjgaVb/NTiRpSvvPQvA4vaX3QaR\nhJCup+InbWOoB7DWnlri85qA8uhVjYeJ/bjeUhBJUg3Nx5i22VQxTOf1FtdxJI1U9HkHtwX/McdJ\nRCTRFO5+A4Dt0cJbZD0M37tDw/wNALYd/mvHaSQRpGupcAq8GQeP+Pnm2Mcs9XnW2rIHNz/c5z8A\nI08Y5igiCSw3r4D2vGcA6L/0ruM0ki4G+npoWGgHoP7w3zhOIyKJJtDkFd6VjNDxjQpvWR+hc/+G\nz1jCvjo2bnnSi9qSDtKyVIh+cn+KR78n9kMesq3BGFNqjHnHGPPgl4t+86iVkcaYeqAR+NEqIotI\nApja+hIABT1nHSeRdNFx7t8ACGb4qazZ5jiNiCSa3LwCbkYL77uXVXjLOmn3Xvru3/ii4yCSKNKy\nVIj6EXDswbcVjDG/A379iKsPPwF+xgPXJ2IbHR4sFqKFwkng58u4SiEiCWpT4w8A2DHzNdOT447T\nSDrwhbw/bu5V6+AmIg83vfVlAAp6PnEbRNJCZHER/9h5AEr2veU4jSSKtJ34ZK0dMcYcBN4xxozg\nrY/0Ayettb9+xC87hbcR4rcPed4vjTHHokMby/HmKIwAP9IaSZHUsHXHfvqpYKMZ5MqFD9j3yuPm\nvYqszsL8HIHxCwCUPfMDx2lEJFFtanwLbv4f7Ji5ytTEKPmFJa4jSQoLfvUpOxhj3ObRcPBV13Ek\nQaRtqQBescAyRuVGy4Gyx/z8KZY3i0FEkojx+egqf5aNQ//O9LU/gUoFWUPBi2d4iklGKaCh8RXX\ncUQkQW3dsZ87VLHJ3OPyl39i//H/yXUkSWGDl/4IQHtRM43ZOY7TSKJI5+sPIiLLlr37bQC2DZzV\npG1ZU8NXvPvRwaLDZGiVpIg8gvH56K7yZv7MffNHx2kk1VXc8a7ZLNZrI5F8T6WCiMgyPHX0baZt\nNtUMEL56znUcSWFV0VWSEa2SFJEnyN/rFd71w58TWVx0nEZS1WD/LQLz3kaiuiPaSCTfU6kgIrIM\nufmFfFtNDKuvAAAgAElEQVTQBMDdtj84TiOpaqC3i8BiCID6ozq4icjj7Tx8ggmbRyUjtF/SwEZZ\nG+HoKslQRj1VNXWu40gCUakgIrJM8/43AKi8fdpxEklV4fNeYdWe2UDFxi2O04hIosvOyeVG0WEA\nhi6p8Ja1YYLe6Li72kgkD1CpICKyTPXP/QMRa2hYaOfu7Q7XcSQFZYa8g9vAppccJxGRZGF3nACg\n+s7HjpNIKlpcWKBh3Lv2WapVkvIAlQoiIstUWV1Le9ZOADq++B+O00iqWZifIzDRAkC5VkmKyBI1\nPPd3LFgf2yNd3A5fdx1HUkz7xY8pYZIxbSSSh1CpICKyAsNbXgMgN/yB4ySSam62fUQxUwxTRGC/\nXjEVkaUpqdjIjZzdAPScU+Et8RXbSNRe2ExmVrbjNJJoVCqIiKzAxkN/B8BTU5eYmhh1nEZSyeiV\nPwEQKtYqSRFZnvFtxwEo7DrpOImkmqroKslI4LjjJJKIVCqIiKxA3VMH6TUbyTHz3Pji313HkRSy\nof9T7zs6uInIMm0+/PcA7Jz5mtHhAcdpJFUM9HV/t5Fou1ZJykOoVBARWQHj89Fd5Q3Rm//mT47T\nSKq4e7sD/2IHEWvwa5WkiCxTbWAvXb5asswi7V/8i+s4kiLCX0Y3EmUEqKyudZxGEpFKBRGRFSrc\n91cABEY+Y3FhwXEaSQWd5/4VgPasHZRVbXKcRkSSUe/G6BC9b99zG0RSRkZ0I9GgNhLJI6hUEBFZ\noZ2H3mCMfMoZo/3SGddxJAWUf/P/ADBU87LbICKStMr2e4X3jvFzzM/NOk4jyW5+bpaDE2cAKH1G\nqyTl4VQqiIisUFZ2Du1FRwAYvvQHx2kk2c3NzrBp4TYA5fvedJxGRJJVw8FXGaaYYia58f+3d+dx\nUlZ3vse/p/d9Y9+hG+hmhwZEUYzKYkxM4gKaxajxJpjMnZk7M7nBcZbEbNdgbpLJzNyZiCY6Scao\n4JJEE2VxIYog0OzQDd1szU7TNPS+1bl/VGFapLfqqjq1fN6vV71auqqe+npOPV1P/Z7nnLN5tes4\niHD7t6yTJDXYZI2bcYPbMAhbFBUAoA9s4S2SpCGn3nScBJGubNPrSjdNkqRxM7jEFIB/4hMSVJ5z\nrSSpbgcTCaNvane+IkmqSJnIikToFEUFAOiDcXNvV6uN12hPpY6V73YdBxGsfpf34P/93E8qLj7e\ncRoAkSx+wiclSSPPviXr8ThOg0g25Ix3KcmWaV90nAThjKICAPRBdt4AlaVMkSQd2/Si4zSIVNbj\n0ciq9ZKkxAmMWQXQN4VzP6Vmm6ih9rSOlJW4joMIdax8t0Z5jqnVxmvc3Ntcx0EYo6gAAH1UN2qB\nJCnzyFrHSRCpjpZt01B7Ws02UYVzP+U6DoAIl56Zo9LU6ZKkk++ztCT8c8z33ilLmaKsnH6O0yCc\nUVQAgD4acfUdkqTC5l26UH3WcRpEohObvUtJlqZOV1pGtuM0AKJBU/7NkqTcynWOkyBSZfhOllw6\neQJ0hqICAPTRsPxJOhw3UgnGowPvMgQCvZdT6T1waxqz0HESANFi9FxvwXt8a6mqTlU6ToNIc7Hm\nnAqbdkmShl91u+M0CHcUFQAgAE4OvlGSZPb/0XESRJrzZ09qfMs+SdKoa+5wnAZAtBg0vEAH4scq\nzlgd2kDBG71zYMPLSjTtOhI3XMPHTnYdB2GOogIABEBu8WckSeMvblRLc5PjNIgk5RteUryxOhg3\nWoNHjnMdB0AUqRo2X5KUUP6a4ySINLbUe5Lk5ECWOEb3KCoAQACMn3GDzilbmaZR+99/3XUcRJC4\nA973y+khNzpOAiDaDJjpLXgX1m9VU0Od4zSIFO1tbRp78T1JUtY0Jg9G9ygqAEAAxMXHqyLnWklS\n3c7fO06DSNHS3KTxtZskSXkzPu04DYBoUzDlGp1WP6WZZpVtfMV1HESI/VvXKUd1uqB0jZ8133Uc\nRACKCgAQIIkTPylJGln1tqzH4zgNIsH+919XpmnUOWVr3AwuMQUQWCYuTof7e/+2NO1+1XEaRIqa\n7b+TJB3IukYJiUmO0yASUFQAgAApnPspNdlEDbVndHjfZtdxEAHqdnkP8ityrlVcfLzjNACiUerk\nWyVJ+dV/kqe93XEaRIIhp9/2/kfhx90GQcSgqAAAAZKWka3StJmSpFObX3KcBuHOejwaftZ74JYw\n4ROO0wCIVoVX36J6m6IBOq/yHe+4joMwd/zgPo32VKrNxmncXJaSRM9QVACAAGrOXyRJyjv2huMk\nCHdH92/XcHtKLTZBhXOZCAtAcCSnpKks4ypJUnXJbx2nQbir3PiCJKksebKyc/s7ToNIQVEBAAIo\n/9o7JUmFbWWqOnXUcRqEs5ObX5YklaZOV3pmjuM0AKJZ+zjvZewDTlLwRtfSj6yVJNWOWuA4CSIJ\nRQUACKABQ0drf8J4SdLBd19wnAbhLOvoOklS45iFjpMAiHZjr71D7daooP2QTh4pcx0HYar2QrUK\nm3ZKkobNucNxGkQSigoAEGDnht0kSUqqeN1xEoSrC+dOq7BljyRp5NWMWQUQXLkDhqgsaZIk6eh7\nLzpOg3B1YMNvlWTaVWmGasTYKa7jIIJQVACAABs021vdL6rfosb6WsdpEI72v/OC4o3VobjRGjKq\n0HUcADHgou9y9rRDqx0nQbjy7POuSHR8IEsco3coKgBAgI2ZOFunNEApplVl773iOg7CUELZ7yVJ\np4YxZhVAaAy9yntVVGHTDtVeqHacBuGmualBhRe8q4PkFDP0Ab1DUQEAAszExelI/+slSS17KCrg\nw+ountfE+s2SpMFX3+U4DYBYMXL8dFWaoUoy7dr/LqtA4MNKN7yiTNOos8rV+FnzXcdBhKGoAABB\nkDbVu0Rg/vl35Glvd5wG4aTsTy8o2bSq0gzV6AmzXccBEEOOD7pRkmRLX3WcBOGmeedLkqSD/W9U\nXHy84zSINBQVACAICufcojqbqv6q0YFtb7uOgzBi9nnPEB4bskAmjo9hAKGTNf3TkqRxFzeorbXF\ncRqEi9aWZo2vWS9JSp/B0Af0HkczABAESckp2p95lSSpetvvHKdBuGisr1VR7SZJUv+rGPoAILTG\nz7xJNcpQtuq1f8s613EQJko3vqYc1alaWSq66mbXcRCBKCoAQJB4xt8iSRp88k3HSRAuSt95UWmm\nWSfMQI2deq3rOABiTEJikg5kz5UkXdzOvArwatjxgiSpPO9jSkhMcpwGkYiiAgAEybhr71CbjdMY\nz2GdOFTqOg7CQPse71UrRwfOZ+gDACfiiz4hSRp+5i1Zj8dxGrjW3tamsefekiSlTL3dbRhELI5o\nACBIsvsNUlnyJEnS0Y0vOE4D15qbGlR04V1JUs6sxY7TAIhV46+9TS02QcPtSR09sNN1HDhWtnmN\n+umCLihdE+be6joOIhRFBQAIotpRCyVJGYdXO04C1/a9+ztlmEadUZ7GF9/oOg6AGJWRlavS1OmS\npJObKHjHutqSVZKk/dnzlJiU7DgNIhVFBQAIomFzvLMoFzbt0sWac47TwKXWXS9Lkg4NuInlugA4\n1TjGW/DOrmSyxljmaW/XmLNvSJISGfqAPqCoAABBNGLsFB2JG65E064D777kOg4c6bhcV8aMOx2n\nARDrRl3j/Ts0vmWvqs8cd5wGruzf9pYGqlp1NlUTrv206ziIYBQVACDITgy6QZJky/7oNgicKX3v\nVWWrXueUraKrFrmOAyDGDR45ThXx+Yo3VhUbKHjHqprNKyVJpVlzlZyS5jgNIhlFBQAIstzpn5Ek\njb/4nlpbmh2ngQsNO7wH7eX9blB8QoLjNAAgnRl6kyQp/sBrjpPABevxaOQZ7/CX+MmfcZwGkY6i\nAgAE2biZN+m8spSlepVtZsLGWNPe1qZx1W9JktKmMWYVQHjoP/M2SVJR3ftqaqx3nAahVr7zXQ21\nZ9Rgk1V03R2u4yDCUVQAgCCLT0hQefZcSVLdzlccp0GolW56XXm6qBplqOjqT7iOAwCSpLFTr9UZ\n5SnNNGv/RobnxZqq931DHzLnKDU903EaRDqKCgAQAgkTvV8mh595S9bjcZwGoVS3zbtk2/6c61mu\nC0DYMHFxOtRvniSpcffvHadBKFmPR8NPrpEkeSYwQSP6jqICAITA+LmfUYtN0HB7SkfLtrmOgxDx\ntLcrv8q7XFfyVMasAggvKZNulSSNObeegncMObxvs0bYE2q2iSqat9h1HEQBigoAEALpmTnalzpD\nknTi/Rcdp0Go7N/6hgbovGptqormcjYIQHgpvOaTarDJGqhqVeza4DoOQuTURu/Qh73ps5WRles4\nDaIBRQUACJGm/JslSbmV6xwnQajUbF0lSSrLvpblugCEnZTUdJVlzJYknd3ysuM0CJUhx1+XJLWN\nv9VxEkQLigoAECKj53pnVx7fWqpzp485ToNgsx6PRp32FpDiJt3mOA0AXFnrWG/Be8CJNxwnQSgc\n3b9doz1H1WrjNf76u1zHQZSgqAAAITJoeIHK4wsUZ6wOvvuC6zgIsvId72iIzqrBJmviPJaSBBCe\nCubeIY81GtteoVOV5a7jIMhObHhekrQvtVjZeQMcp0G0oKgAACF0dvhCSVJK2UuOkyDY/rxc19VK\nSctwnAYArqzfoOEqS5ooSTr81i8dp0Gw9a98TZLUNO6TjpMgmlBUAIAQGvmx+yVJk5q26/SxCrdh\nEDTW49GIU97luuxEVn0AEN4ujr9TkjT40EusAhHFjh/cp7HtFWqzcRp3/Wddx0EUoagAACE0LH+C\n9iZO9g6BWPcL13EQJIf2btZwe1JNNlFF8+50HQcAulS04D4120SN9hxlFYgoVrnhWUlSacpU5Q4Y\n4jgNoglFBQAIsbqiJZKkoUde5oxQlDqz8TlJ0r702UrPzHGcBgC6lp3bX7szr5UkVb3ztNswCJrc\nw3+UJNXnf8JxEkQbigoAEGITFtyrRpukUZ5jOrD9T67jIAgGn1gtSWov+rTjJADQMwnFX5AkFZ59\nXa0tzY7TINBOVZarsK1MHmtUMI+hDwgsigoAEGKZ2Xnak329JOn8hqfdhkHAHSkt0WhPpVpsvMbN\nW+I6DgD0yKR5t6lKOcrVRe15mxWKos3hP3mHPpQlTVT/oaMcp0G0oagAAA4kFX9eklRYtVrNTQ2O\n0yCQTrznG/qQWqzs3P6O0wBAzyQkJql80C2SJM/2ZxynQaBlHfIOfbgw5hbHSRCNKCoAgAOTrvuM\nzihPOarT3rdXuo6DABp4zDv0oWX8pxwnAYDeGTjvS5KkyXUbVFN1ynEaBErVqaMqatkjSRp9HUMf\nEHgUFQDAgfiEBFUM8U2UtONZt2EQMMcP7lFB+0Hfcl13u44DAL2SP3mOKuLzlWTaVbbuv1zHQYBU\nrH9WccZqf8J4DR45znUcRCGKCgDgyJDrfWeE6jep+sxxx2kQCJXveAtE+1KmKaf/YMdpAKD3zhbc\nIUnKPbDKcRIESnrFq5Kk6lEMfUBwUFQAAEdGT5ilA/FjlWjatX/d067jIADyjr4mSWoo+KTjJADg\nn7E33a82G6fxbft1pGy76zjoo/NnT6qoaackacS1n3OcBtGKogIAOHRu7J2SpP7lzLQd6U4dPaDx\nbfu9y3Ux9AFAhOo/eIR2p10lSTrx9s8dp0FfHVj/nBKMRxXx+RqWP8F1HEQpigoA4FDhgi+pxcZr\nbHuFDu3d7DoO+uCwb+hDafJk9R880nEaAPCfZ6p3Mr/8E6+qva3NcRr0RfKBVyRJZ0bc7DgJohlF\nBQBwKHfAEO1Jv1qSdHr9U47ToC+yD/1BknSR5boARLhJN96tC0rXIJ3T3g2vuo4DP104X6UJjSWS\npKHXsOoDgoeiAgC4Nv3zkqSCU39QW2uL4zDwx+ljFSps2SdJGjOPAzcAkS05JU2l/RZKkpq3/Mpx\nGvhr/9vPKsm063DcSI0qnO46DqIYRQUAcGzSxxbrvDI1QOe1953fuY4DPxxcs0Jxxmpv4mQNGl7g\nOg4A9Fn2NfdKkiZeWK+6i+cdp4E/MvY8I0k6OeITjpMg2lFUAADHkpJTtL//IklSS8kzjtOgtzzt\n7Rp9xDvRZsOUexynAYDAKCy+UZVmqNJMs/au+7XrOOilI6UlmtC6R202TgWLvuo6DqIcRQUACAN5\n194vSZp8cb0u1pxzGwa9svtPL2uIzuqi0jV5wRddxwGAgDBxcTo+6nZJUvq+5x2nQW+dfHOFJGlX\n+tUaOGyM4zSIdhQVACAMjJ12nQ7HjVCKaVXpul+6joNeaNv8tCRp34BblJKW4TYMAATQ6Ju+JI81\nmtSyUycOl7mOgx5qbmpQ4Wnvqg9m5n2O0yAWUFQAgDBg4uJ0crT3jFBm6UrHadBTVacqNaXuXUnS\nwBuWOk4DAIE1eOQ47U2ZJkk68uYvHKdBT+1a99/KVa3OKE+Tr7/DdRzEAIoKPsaY5caYBX3cRo5v\nO8uNMcuMMY8bYzjKBNAjBfMfULs1mtC6R8cP7nEdBz1wYPUKJZp2lSUUacykOa7jAEDANU64S5I0\n4uhvZT0ex2nQEyk7vXNgHBx+uxISkxynQSyI+aKCMabYGLNS0jJJOX3YTo6krZKes9Y+ZK19zFr7\noKQCY8zjAYoLIIoNHDZGe1KLJUlH33zKcRp0x3o8GnHIe1XJxYmfd5wGAIJj4vwvqMEma7g9qbIt\n61zHQTeOH9yjyc3b5bFGoxY+6DoOYkTMFhWMMUuNMWsk3S1pTQA2uVLSKmttScdfWmsfknRXX6+C\nABAbWibdLUkadex38rS3O06Drux571UNtydVZ1M1adH9ruMAQFCkZ+ZoT86NkqQLG5nzJ9wdXfsz\nSdLu1FkaMqrQcRrEipgtKlhrV1hrF/q+9G/py7aMMfmSFkjq7IqE5yUt78trAIgNk276vOpsqoba\n0yp9f7XrOOhC80bv+OI9/RcpLSPbcRoACJ7U2V+QJE2oXqumhjrHadCZ1pZmjTvxO0lS+wxWI0Lo\nxGxRIcAWS5K19mAn91dIKvYNkQCATqWmZ2pvrveMUN37v3KcBp05f/akplxcL0nqdz1T5wCIbhOv\n+aROaYCy1KA9bz3nOg46sfvNZ9VfNapSjibf+FnXcRBDKCoExkJJNV3cf6nYMKsvL3Lx4sUe3Zqb\nm/vyMgAcy5hzryRpYvUbaqyvdZwGV1K2+gklmTaVxxdo7LTrXMcBgKCKi4/XoWG3SpISdj3rOA06\nE7/NezLiwNBPKzEp2XEaxBKKCoGRJ6m6i/svFRzy+/IiQ4cOVXZ2dre3Rx99tC8vA8CxoqsW6YQZ\npAzTqD1vPOM6Di5jPR4NqXheknSu8HOO0wBAaAy/4UuSpEkNW1R16qjjNLjcySNlmtzoHdE9csFX\nHadBrElwHSBKdDes4VLBoU/DH06cOKH09PRuH5ecTGUSiGRx8fE6MvxTGlr5pJL2PCd9itmbw0nZ\n5rUq8lSqwSZr4s3/w3UcAAiJEeOmqSyhSIVtpSpf+wv1v+cR15HQweG1KzTEWO1Onq7J+ZNcx0GM\n4UqFwMhT18MfLunXlxfJysrq0Y2iAhD5Rt74gCRpUmOJzhw/5DgNOqrd8KQkaXfufGVm5zlOAwCh\nUzN+sSRp4MGXHCdBR22tLSqofFGS1DT1HsdpEIsoKgQGEzACCKhh+ZO0L3GS4o3VwXW/cB0HPhfO\nV2lyzZuSpKzrvuw4DQCEVtGC+9VsE5XvOayKnRtcx4HP7vUvaqCqdV6ZmjL/C67jIAaF/fAH34oJ\n+fJeDeCPamttSQAjXUmNelZYOBfkHACiSG3REmnXHg0+/JKs59sycdSBXStd/aTmmBYdihulwuIb\nXccBgJDKzhugksy5Kq57W2ffeVoFU+e6jgRJdut/SZLKBt2qq1PSHKdBLAr7ooKkpZL6OqC4IBBB\nutDVJI3SnwsiPRkiAQCSpKL596pp5/c12lOpAzve0bgZ17uOFNOsx6MBZb+RJJ0ed7fGUOQBEIPi\nZnxe+tPbGn/mj2ptaWaVAcfOHD+kKfUbJSMNuZEljuFG2B8RWWsfs9YW9OUWgpgl6nplh0tXMRzs\n4jEA8CFZOf20J2ueJKl6w385ToMD29cr33NYTTZRExYx9AFAbJo073adU7bydFF7/sTcCq5VrP6Z\nEoxH+xInaVRRses4iFFhX1SIEGu6uT9fkqy1a0OQBUAUSSz2jo0cf/Z1tTQ3OU4T22r+9IQkaXf2\nDcruN8hxGgBwIzEpWQcG3SJJ8mz7b8dpYpunvV2jjnonaKybxFwKcIeiQmCslSRjTGflwdmXHgMA\nvTFp3m06q1zlqlZ73l7lOk7Mqrt4XpOrvfXjtGtYRhJAbBtw3ZckSZNrN+jCudOO08SuPe/8VkPt\nGV1UuqYsus91HMQwigq9YIzJMcYsN8Ys6Ph7a+1BeYsGnc39sFjS8mDnAxB94hMSVDH4E95/bH/G\nbZgYtnf1U0ozzToaN0wT5tzsOg4AOFUw5WpVxI9RkmlT6TqG57nSuvkpSdK+/h9XSlqG4zSIZRQV\nvPIu+9mZpZKW6crDHZZIWnD51QrGmJWSVjD0AYC/Bl3vPSM0qX6jzp896ThNbMot9RZ0TuTfxSoc\nACDpbP7tkqSc/S84ThKbqk5Vakrtu5KkATf0dU57oG9i9sjIGLPYGLPGGFOhPxcJHjfGVPh+v/gK\nT1sr7woOKy6/w1pbI2mmpAd9VzMsM8Y8LmmNtZY9HYDfxkycrfL4AiWZdu1f97TrODGnYucGjWs7\noBYbr/GLvuI6DgCEhbHzH1CbjVNhW6mO7t/uOk7MKV+9QommXfsTxit/8hzXcRDjImFJyaCw1q6S\n1KsBytbaEkm5Xdxfo74vfwkAH1E19k6NLXtMeeUvSHrYdZyYUrX+CRVI2pU5TzMHDnMdBwDCQv/B\nI7QjbbamNW7S8bef0sjxP3UdKWZYj0fDDnm/xtRM+LzjNEAMX6kAAJFk/Pz71WrjNa7tgI7s2+o6\nTsxorK/VxLN/lCQlXfWA4zQAEF7apnxOkjTm+CvytLc7ThM79r73R42wJ1RvUzRp0ZdcxwEoKgBA\nJMgbOEy7072XN55Y/7TbMDFk1+qnlWkaddwM0qRrb3UdBwDCyqQb79JFpWuwqrT3vVddx4kZjRt/\nLkna3W+R0jNzHKcBKCoAQOSY9llJUsHJV9Te1uY4TGzI2uudoPHo6MWKi493nAYAwktKarr29fMu\nita4+deO08SGmqpTmnrxbUlS3jzm+UF4oKgAABFi4seWqEYZGqhq7X33d67jRL3D+7aoqHWv2myc\nxi1kuhwAuJLsq++VJE2qeUv1tTWO00S/0tVPKMm0qSI+X2OnXec6DiCJogIARIzklDSV9V8kSWre\n+t+O00S/U296F/rZlX6N+g8d5TgNAISnwpk3qdIMVZpp1t51fDYFk/V4NLj8OUlSVeHnWOIYYYN3\nIgBEkNy590mSJl1Yr9oL1Y7TRK+mxnoVnfGOD46bzSRYANAZExenYyM/LUlK3fe84zTRrWzLOo32\nVKrBJmvCov/hOg7wAYoKABBBxk2/XkfihivVtKh03a9cx4lau9f+Wjmq0ykN0OR5t7uOAwBhbfRN\n3tVxJjbt0KmjBxyniV617z4pSdqTe5Oycvo5TgP8GUUFAIggJi5OJ0bdJklKL13pOE30St3lnXDs\n0MjbFZ+Q4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "element_LGL_flat = af.flat(params.element_LGL)\n", + "E_z_init_flat = af.flat(u_init[:, :, 0])\n", + "B_y_init_flat = af.flat(u_init[:, :, 1])\n", + "\n", + "plt.plot(element_LGL_flat, E_z_init_flat, label = r'$E_z$')\n", + "plt.plot(element_LGL_flat, B_y_init_flat, label = r'$B_y$')\n", + "\n", + "plt.title(r'Plot of $E_z(t = 0)$ and $B_y(t = 0)$')\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "\n", + "plt.legend(prop={'size': 14})\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Prototype implementation of RK4 for multiple-u's" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "u = u_init[:, :, :]\n", + "\n", + "shape_u_n = utils.shape(u)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "A_inverse = af.tile(af.inverse(w1d.A_matrix()),\n", + " d0 = 1, d1 = 1,\n", + " d2 = shape_u_n[2])\n", + "\n", + "\n", + "k1 = utils.matmul_3D(A_inverse, w1d.b_vector(u))\n", + "k2 = utils.matmul_3D(A_inverse, w1d.b_vector(u + k1 * params.delta_t / 2))\n", + "k3 = utils.matmul_3D(A_inverse, w1d.b_vector(u + k2 * params.delta_t / 2))\n", + "k4 = utils.matmul_3D(A_inverse, w1d.b_vector(u + k3 * params.delta_t))\n", + "\n", + "delta_u = params.delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6\n", + "\n", + "# print(delta_u)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\r", + " 0%| | 0/626 [00:00\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mw1d\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime_evolution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu_init\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/workspace/quazar/git/amanabt/DG_Maxwell/dg_maxwell/wave_equation.py\u001b[0m in \u001b[0;36mtime_evolution\u001b[0;34m(u)\u001b[0m\n\u001b[1;32m 805\u001b[0m \u001b[0mu_analytical\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manalytical_u_LGL\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt_n\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 806\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 807\u001b[0;31m \u001b[0mu_diff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mu_analytical\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 808\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 809\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/anaconda3/lib/python3.6/site-packages/arrayfire/array.py\u001b[0m in \u001b[0;36m__sub__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 850\u001b[0m \u001b[0mReturn\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 851\u001b[0m \"\"\"\n\u001b[0;32m--> 852\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0m_binary_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maf_sub\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 853\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 854\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__isub__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/anaconda3/lib/python3.6/site-packages/arrayfire/array.py\u001b[0m in \u001b[0;36m_binary_func\u001b[0;34m(lhs, rhs, c_func)\u001b[0m\n\u001b[1;32m 173\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Invalid parameter to binary function\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 174\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 175\u001b[0;31m \u001b[0msafe_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc_pointer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlhs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_bcast_var\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 176\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 177\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/anaconda3/lib/python3.6/site-packages/arrayfire/util.py\u001b[0m in \u001b[0;36msafe_call\u001b[0;34m(af_error)\u001b[0m\n\u001b[1;32m 77\u001b[0m \u001b[0merr_len\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mc_dim_t\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[0mbackend\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maf_get_last_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc_pointer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc_pointer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr_len\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 79\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mto_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr_str\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 80\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 81\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_version\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mRuntimeError\u001b[0m: In function af::dim4 getOutDims(const af::dim4&, const af::dim4&, bool)\nIn file src/backend/ArrayInfo.cpp:178\nInvalid dimension for argument 1\nExpected: ldims == rdims\n" + ] + } + ], + "source": [ + "w1d.time_evolution(u_init)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb new file mode 100644 index 0000000..0f700c6 --- /dev/null +++ b/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb @@ -0,0 +1,256 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1193: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n", + "/home/ubermensch/.local/anaconda3/lib/python3.6/site-packages/numpy/lib/polynomial.py:1220: FutureWarning: In the future extra properties will not be copied across when constructing one poly1d from another\n", + " other = poly1d(other)\n" + ] + } + ], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../../'))\n", + "\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "import arrayfire as af\n", + "\n", + "from dg_maxwell import params\n", + "from dg_maxwell import lagrange\n", + "from dg_maxwell import wave_equation as w1d\n", + "from dg_maxwell import utils\n", + "\n", + "af.set_backend('opencl')\n", + "af.set_device(1)\n", + "af.info()\n", + "\n", + "plt.rcParams['figure.figsize'] = 12, 7.5\n", + "plt.rcParams['lines.linewidth'] = 1.5\n", + "plt.rcParams['font.family'] = 'serif'\n", + "plt.rcParams['font.weight'] = 'bold'\n", + "plt.rcParams['font.size'] = 20 \n", + "plt.rcParams['font.sans-serif'] = 'serif'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['axes.linewidth'] = 1.5\n", + "plt.rcParams['axes.titlesize'] = 'medium'\n", + "plt.rcParams['axes.labelsize'] = 'medium'\n", + "\n", + "plt.rcParams['xtick.major.size'] = 8\n", + "plt.rcParams['xtick.minor.size'] = 4\n", + "plt.rcParams['xtick.major.pad'] = 8\n", + "plt.rcParams['xtick.minor.pad'] = 8\n", + "plt.rcParams['xtick.color'] = 'k'\n", + "plt.rcParams['xtick.labelsize'] = 'medium'\n", + "plt.rcParams['xtick.direction'] = 'in' \n", + "\n", + "plt.rcParams['ytick.major.size'] = 8\n", + "plt.rcParams['ytick.minor.size'] = 4\n", + "plt.rcParams['ytick.major.pad'] = 8\n", + "plt.rcParams['ytick.minor.pad'] = 8\n", + "plt.rcParams['ytick.color'] = 'k'\n", + "plt.rcParams['ytick.labelsize'] = 'medium'\n", + "plt.rcParams['ytick.direction'] = 'in'\n", + "plt.rcParams['text.usetex'] = True\n", + "plt.rcParams['text.latex.unicode'] = True" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Set the initial conditions\n", + "\n", + "E_00 = 1.\n", + "E_01 = 1.\n", + "\n", + "B_00 = 0.2\n", + "B_01 = 0.5\n", + "\n", + "E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + E_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \\\n", + " + B_01 * af.cos(2 * np.pi * params.element_LGL)\n", + "\n", + "u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2, dtype = af.Dtype.f64)\n", + "u_init[:, :, 0] = E_z_init\n", + "u_init[:, :, 1] = E_z_init" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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/znYkERHphY/ff4H5p58HoGLRj4gbnGg5Ue+ljhxL42fXU+PEML1hN9ue/7nt\nSCIiYWf79u1kZWW1e999992H2+0mPz8/yKnap6KC9DtFv/s6qVRyyDWGKx581HacPouNG4y5679p\nclzMqX6LnW+ssx1JRER6oKa6iqF5fw/A5pS7mHH1nZYT9d24zMvZNdm7I8SU3f9BedkRy4lERMJL\nXl4eixcvbvc+t9sNQFJSUjAjdUhFBelXdr7xHHOrXsfjGGpv/Rmxg+JtR/KLjFlXsm3U/QAMf+ef\nqKmuspxIRES6a9fvvsNlzgnKSGXaQz+1Hcdvsu/9R4ojMkjgPAd//03bcUREwkZlZSVut5slS5a0\ne9+jjz7K4sWLSU9Pt5DuUioqSL9xtvI0o97x7vu9ZeRnmZK9yHIi/5r1+UcpYxijOMXOZ/7JdhwR\nEemGfZtfZ96J9QCcvO4xhiQmW07kP5FR0Ti3/5Rmx5B9No/d7/zJdiQRkbCQl5cHQHZ29kW3u91u\nFi1aRHZ2NuvXr7cRrV0qKki/se/Jv2U4FRw1o5j90H/YjuN3cYMTKbvGu4vF3NLf4/54s+VEIiLS\nmbqaauJf/TtcxmFL0q3Muu4e25H8btIV17J1+FIAhr75j9TVVFtOJCIy8G3dupWkpCTWrVvHmjVr\nWLNmzYWdHx555BFyc3NDZuoDQKTtACLdsfudPzHvzIsAnL3xJ4yOH2I5UWBcvuiz5O94hqzqd2h8\n/ht4pn6IKyLCdiwREWnHjqdWsdAp5RRDyXxo4C5mOP3zj3HyJxsZ7ZTx4TP/h4UPD5wpHiIioSgv\nL4/ly5ezfPnyC7ctX76cyspKFi1aRFJSUofrLdigkQoS8qrPniH1jX8AYHPqPUxbeIvlRIE15nP/\nRbUziMymQrb+oX9uSSYiMtAV5b/FvNJnADh21b+RmDzMcqLAGZKYzNGFPwBgztHfcXDvNsuJRCSs\nOA40nA/9L8fx20vOz89n7ty5l9zeUkxob60FmzRSQUJewe++zXxOUWqGM+MLP7YdJ+CGpY1n87Rv\nMn/vo1xRkEPpgTtJmzDFdiwREfGpr6sh+sVvEGEctiUsJnvJ52xHCrgrljzAjp2/54qaD3DWfwnP\nP+/QSDoRCY7GGvi3NNspuvZPpRDd90XkW9ZT6GgkQkZGBuAtPHS05WSwaaSChLSCD15mfvkfAai4\n4UfEDwmduUOBlH3PdyiKnEy0aeLY89+1HUdERFrJf/qfGe85zGkSmfjQL2zHCQrjcjHqsz+nxolh\ngucQ+S89YTuSiMiAlJ+fT1JSUodrJuTm5gKETEEBNFJBQljt+XMk5n4LgC3JdzDvmrssJwqeiMhI\nGm/4F3j9fuZUvs6Bgs1MmD4WDDHiAAAgAElEQVTfdiwRkbBXvPN95h75XzBwaP6/kJU60nakoBk5\ndhKbRn6GBSeeJW3Hj2m46YtEx8TajiUiA11UnHcUQKiLivPLYXJzczscpeB2u9mwYQMrV668cNua\nNWvYvn07q1atIj09HbfbzYoVKy4UH4JBIxUkZO383XcY7ZRxghSmPPQz23GCbvqVt5I/+FpcxqHq\npe/ZjiMiEvYaG+oxf/k6kcZDfvy1ZN3yV7YjBd2sB3MoJ4k05wQ7/vQT23FEJBwY451WEOpfxvjl\n5ebl5bW7nkJ+fj5Llixh8eLF5OTkALBhwwbuvfdeKioqcLvdF56fnp7ulyzdpZEKEpL2bcllXtla\nMFB27b8zOynFdiQrUu/8IU3PXM/lNR+yb/PrTJl/o+1IIiJha9sz32Vhs5tKBjP2wV/ajmNF3OBE\ndk/7Gql7/pWJ+x7n/LmvhM3URBGRQFqxYgXbtnkXwl27di0lJSUX7mspGOTk5LB06dILt7f8OS8v\nj/Xr1wPekQ733XdfsGIDKipICKqrPU+cb9/vrYk3MfeGe21Hsmbs5MvZknIb8ypewMn7Ps7cxRiX\nBhiJiATbgT1bmXPwCTBQnPV/yR45xnYka7I+/Xcc3fsb7xaTGx5l4V/l2I4kItLvrV69ulfP27Bh\nA9nZ2Rd+zsvL44kngrvujXonEnJ2/O4fGes5RjlJTH7ov2zHsW78PT+kzoliamMBu95aZzuOiEjY\naWpsoPGPXyXaNPNR3ELm3L686ycNYFHRMZRlfweAmQefpOLkMcuJRETCV0VFxYVFG/Pz8wE6XOQx\nUFRUkJBSlP8280qfAuDIlf9KYsoIy4nsG37ZBHakeYcwJbz3KM1NTZYTiYiEl23P/pDJTUWcJY60\nBx7XiDEg6+YvURyRwWBTS9EffmA7johI2Lr33nuprKxkw4YNrFq1qsNFHgNJ/ytKyHA8Hnj5O0QY\nh+1DbuCKGz9vO1LImLb0u5wlngmeg+x4Wdt4iYgES3npIS4veRyAfbMfYfhlEywnCg2uiAhqrvln\nALLKNnD8UKHlRCIi4SkpKYnVq1ezdOlSkpKSgr6eAqioICFkz6ZXmdxURJ0TxbgHfm47TkhJTBlB\nwQTvKuNpO35MfV2N5UQiIuFh/0s/JtY0Uhg5hbl3fd12nJAy89q7KYieTbRp4ugfv2s7johI2Kms\nrCQjIwPwTn1wu90XLeQYLCoqSMhofNe7beTO1NtIDeMFsDpy+dJ/5BRDSXNOsuNPP7UdR0RkwKup\nrmLaMe9q2ufnfl3THtowLheRN34fgDmVr3Fgz1a7gUREwkxSUhKrVq1izZo1rF27lo0bN1rJod0f\nJCQcKvyIy2s34XEMaTd/23ackDQofgi7pn+dYQU/ZFLhr6ir/TtiB8XbjiUiMmDtfvGXzOc8R81I\nZi+633ackJSZfQP5b15D1vl3OfPSD5gw7QXbkUREwsry5fYXD1bJXULCidd+BMDO+IWMmTTbcprQ\nlXXXNyhjGClUsfuVX9uOIyIyYDU3NTGm8LcAHJvyJSIidR2mI0Nv+x4As6vfpfTAPstpREQk2FRU\nEOvKy44w+/SrAMR+6puW04S2qOgYDk58AIDUj//Hu7iliIj43c7cp0hzTnCGIcy6/au244S0CdPm\nsjsmiwjjcPhVTc8TEQk3KiqIdftf+ikxppGiyMlMmbvEdpyQN/XWr1PjxDDBc5CCD160HUdEZMBx\nPB7it/t2fBi9jEHxQywnCn2e+V8BYHrZ81SfPWM5jYiIBJOKCmJV7flzTDmyFoBzWV/VIljdkJg8\njN3DbgOg6YNfWk4jIjLwFG7NI7OpkAYnkkm3a52f7pj5qXs4YtIYYmr5+KXHbccRkX7McRzbEQY8\nf7/H6sGJVbteepyhnKPUjGD2kgdsx+k30m7yThOZdX4TR4p3W04jIjKw1L7tHcL/UfLN2o2om1wR\nEZRO+SIAo4uexNPcbDeQiPQ7ERERADQ2NlpOMvC1vMct73lfqagg1jQ3NZG217sI1uHJXyAyKtpy\nov5jzKTZ7Bw0H5dxKH1N81dFRPzlSPFuZp//AIARN/295TT9y4xbV3CWeEY7Zex6c53tOCLSz0RF\nRRETE0NVVZVGKwSQ4zhUVVURExNDVFSUX46ppYzFml1vPMcVTilniWfm7V+zHaffcS38GryxmZkn\nX6DqTDmJQ1NtRxIR6fdKX/kRY4zDzkHzmT0ly3acfiV+SBKbRn6aBWXPELn1V7BY23CKSM+kpqZy\n7Ngxjh49SmJiIlFRURhjbMcaEBzHobGxkaqqKqqrq7nsssv8dmwVFcSa2K3e9QAK0paycEiS5TT9\nz4yr7+DgW2MZ7znMppd/wYIHvmc7kohIv3bm1HFmlb8MBiKv/jvbcfql8bd+i6bfPMuM+o9wf7yZ\n9BnzbUcSkX4kISEBgPLyco4dO2Y5zcAUExPDZZddduG99gcVFcSKfds2MrWxgAYngolaBKtXjMvF\nyelfYvzu7zNu/1M0NT6iKSQiIn2w78WfstA0UByRwbSFt9iO0y+NHDuJ/CHXkFX9NuV5PyV9xrO2\nI4lIP5OQkEBCQgKNjY00a30Wv4qIiPDblIfWVFQQK2re8q4DsHPojcxNG283TD8265aHObP7PxnF\nKXa88SxX3PQF25FERPqlutrzTD7k7QBXXvFl7UbUB3HXfgNefpvZZ3I5feIoKSNG244kIv1QVFRU\nQDrA4n/6H1OC7ph7L7PPvQtA6o1aBKsvYuMGs++ypQDEbFtjOY2ISP+16+U1pFBFGcOYfaMKtH2R\nmb2IosjJxJhGil7+L9txREQkwFRUkKA7+sqPiDAOu2KzmTBtru04/d7E275JoxPBtMaP2f/Ru7bj\niIj0O57mZkYU/BqAg5MeJCo6xnKi/s24XJyd/TcATDr0HPV1NZYTiYhIIKmoIEFVdfoEM0++AIC5\n8m8tpxkYhqWNZ2fi9QBUvvlzy2lERPqfXW+tZ5znKOecQUy//Ru24wwIs2/6IidJJpVKdr32v7bj\niIhIAKmoIEG158WfEWfqKYmYwIyr77AdZ8BIvN67Svnsyo2Ulx6ynEZEpH+J2vwLAApGfYYhicmW\n0wwMUdExlEzwbik5dNevcTwey4lERCRQVFSQoKmvq2HSgWcAqJi1XItg+dGkK65lb9Q0ok0zxS//\nzHYcEZF+Y/+Od5jesItGJ4IJt2udH3+aetvfUudEMbG5hL1bXrcdR0REAkS9Ogmana/8mlQqOUky\ns2/+ku04A05t1nIAMo+up672vOU0IiL9w9k3fgLAzsQbGDE6w3KagSUpdSQ7U7xbc9a9+9+W04iI\nSKCoqCBB4Xg8DN/9BADujAeJjom1nGjgmbX4AcoYxlDOsvuVX9uOIyIS8o4fKmT22bcAGLr423bD\nDFAjl3wTgNnV71F6YJ/lNCIiEggqKkhQ7H77j4z3HOa8E8vU27VAYyBERkVzcOIDAKR+/D+avyoi\n0oVDL/+YSOPh45jLyZh1pe0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xREQ6VF52hCkNBQCMv/o+y2kkkNKu+jwA085voer0Cctp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\n0MjbFZ+Q4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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "element_LGL_flat = af.flat(params.element_LGL)\n", + "E_z_init_flat = af.flat(u_init[:, :, 0])\n", + "B_y_init_flat = af.flat(u_init[:, :, 1])\n", + "\n", + "plt.plot(element_LGL_flat, E_z_init_flat, label = r'$E_z$')\n", + "plt.plot(element_LGL_flat, B_y_init_flat, label = r'$B_y$')\n", + "\n", + "plt.title(r'Plot of $E_z(t = 0)$ and $B_y(t = 0)$')\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "\n", + "plt.legend(prop={'size': 14})\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Prototype implementation of surface term for multiple-u's" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(8, 10)\n" + ] + } + ], + "source": [ + "u_n = u_init[:, :, 0]\n", + "# Older surface term code.\n", + "\n", + "L_p_minus1 = params.lagrange_basis_value[:, 0]\n", + "L_p_1 = params.lagrange_basis_value[:, -1]\n", + "f_i = w1d.lax_friedrichs_flux(u_n)\n", + "f_iminus1 = af.shift(f_i, 0, 1)\n", + "surface_term = af.blas.matmul(L_p_1, f_i) - af.blas.matmul(L_p_minus1,\\\n", + " f_iminus1)\n", + "surface_term_ref = surface_term.copy()\n", + "print(surface_term_ref.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Code refactor of the old surface term code to handle multilple u" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(8, 10, 2)\n" + ] + } + ], + "source": [ + "# Arguments\n", + "u_n = u_init[:, :, :]\n", + "\n", + "#####################################################\n", + "######################CODE###########################\n", + "#####################################################\n", + "\n", + "shape_u_n = utils.shape(u_n)\n", + "\n", + "L_p_minus1 = af.tile(params.lagrange_basis_value[:, 0],\n", + " d0 = 1, d1 = 1, d2 = shape_u_n[2])\n", + "L_p_1 = af.tile(params.lagrange_basis_value[:, -1],\n", + " d0 = 1, d1 = 1, d2 = shape_u_n[2])\n", + "f_i = w1d.lax_friedrichs_flux(u_n)\n", + "f_iminus1 = af.shift(f_i, 0, 1)\n", + "\n", + "surface_term = utils.matmul_3D(L_p_1, f_i) \\\n", + " - utils.matmul_3D(L_p_minus1, f_iminus1)\n", + "\n", + "print(surface_term.shape)\n", + "surface_term_test = surface_term.copy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Testing" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n" + ] + } + ], + "source": [ + "print(af.all_true(af.abs(w1d.surface_term_multiple_u(u_n)[:, :, 1] - w1d.surface_term(u_n[:, :, 0])) < 1e-14))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/maxwells_equations/advection_1d_multiple_u_and_f.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_volume_term.ipynb similarity index 100% rename from examples/maxwells_equations/advection_1d_multiple_u_and_f.ipynb rename to examples/maxwells_equations/advec_1d_multiple_u_volume_term.ipynb diff --git a/main.py b/main.py index 3649599..f87445c 100644 --- a/main.py +++ b/main.py @@ -1,13 +1,33 @@ #! /usr/bin/env python3 +import numpy as np import arrayfire as af af.set_backend('opencl') af.set_device(1) af.info() +from dg_maxwell import params from dg_maxwell import wave_equation from dg_maxwell import lagrange if __name__ == '__main__': - u_diff = wave_equation.time_evolution() + # 1. Set the initial conditions + + E_00 = 1. + E_01 = 1. + + B_00 = 0.2 + B_01 = 0.5 + + E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \ + + E_01 * af.cos(2 * np.pi * params.element_LGL) + + B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \ + + B_01 * af.cos(2 * np.pi * params.element_LGL) + + u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2) + u_init[:, :, 0] = E_z_init + u_init[:, :, 1] = B_y_init + + u_diff = wave_equation.time_evolution(u_init) print(lagrange.L1_norm(u_diff)) From 18eb775e3c54e4bcf9b1233fa131cc7ced96d2e2 Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 16:47:43 +0530 Subject: [PATCH 06/13] Initial conditions for Maxwell's added in main.py - Maxwell's equations solved analytically in examples/maxwells_equations/analytical_solution.ipynb and the solution is overlapping with the numerical solution at all t. --- dg_maxwell/params.py | 2 +- dg_maxwell/wave_equation.py | 22 +- .../analytical_solution.ipynb | 343 ++++++++++++++++++ main.py | 1 - post_processing.py | 24 +- 5 files changed, 374 insertions(+), 18 deletions(-) create mode 100644 examples/maxwells_equations/analytical_solution.ipynb diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index 8f58d03..c2d4c0e 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -32,7 +32,7 @@ N_quad = 8 # Wave speed. -c = -1. +c = 1.0 # The total time for which the wave is to be evolved by the simulation. total_time = 2.01 diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 0c80c8c..999ac61 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -196,8 +196,12 @@ def flux_x(u): of numpy.poly1d polynomials. ''' - flux = params.c * u - + #flux = params.c * u + flux = u.copy() + + flux[:, :, 0] = -u[:, :, 1] + flux[:, :, 1] = -u[:, :, 0] + return flux @@ -799,11 +803,15 @@ def time_evolution(u = None): for t_n in trange(0, time.shape[0]): # Storing u at timesteps which are multiples of 100. - if (t_n % 20) == 0: + if (t_n % 5) == 0: h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') - dset = h5file.create_dataset('u_i', data = u[:, :, 1], dtype = 'd') + Ez_dset = h5file.create_dataset('E_z', data = u[:, :, 0], + dtype = 'd') + By_dset = h5file.create_dataset('B_y', data = u[:, :, 1], + dtype = 'd') - dset[:, :] = u[:, :, 1] + Ez_dset[:, :] = u[:, :, 0] + By_dset[:, :] = u[:, :, 1] # # Implementing second order time-stepping. # u_n_plus_half = u + af.matmul(A_inverse, b_vector(u))\ @@ -820,8 +828,8 @@ def time_evolution(u = None): u_analytical = analytical_u_LGL(t_n + 1) - u_diff = af.abs(u[:, :, 1] - u_analytical) + #u_diff = af.abs(u[:, :, 1] - u_analytical) - return u_diff + #return u_diff diff --git a/examples/maxwells_equations/analytical_solution.ipynb b/examples/maxwells_equations/analytical_solution.ipynb new file mode 100644 index 0000000..5c46b31 --- /dev/null +++ b/examples/maxwells_equations/analytical_solution.ipynb @@ -0,0 +1,343 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "import os\n", + "import sys\n", + "sys.path.insert(0, os.path.abspath('../../'))\n", + "\n", + "from matplotlib import pyplot as pl\n", + "from scipy.integrate import odeint\n", + "import numpy as np\n", + "import h5py\n", + "\n", + "from dg_maxwell import params\n", + "\n", + "pl.rcParams['figure.figsize' ] = 9.6, 6.\n", + "pl.rcParams['figure.dpi' ] = 300\n", + "pl.rcParams['image.cmap' ] = 'jet'\n", + "pl.rcParams['lines.linewidth' ] = 1.5\n", + "pl.rcParams['font.family' ] = 'serif'\n", + "pl.rcParams['font.weight' ] = 'bold'\n", + "pl.rcParams['font.size' ] = 20\n", + "pl.rcParams['font.sans-serif' ] = 'serif'\n", + "pl.rcParams['text.usetex' ] = True\n", + "pl.rcParams['axes.linewidth' ] = 1.5\n", + "pl.rcParams['axes.titlesize' ] = 'medium'\n", + "pl.rcParams['axes.labelsize' ] = 'medium'\n", + "pl.rcParams['xtick.major.size'] = 8\n", + "pl.rcParams['xtick.minor.size'] = 4\n", + "pl.rcParams['xtick.major.pad' ] = 8\n", + "pl.rcParams['xtick.minor.pad' ] = 8\n", + "pl.rcParams['xtick.color' ] = 'k'\n", + "pl.rcParams['xtick.labelsize' ] = 'medium'\n", + "pl.rcParams['xtick.direction' ] = 'in'\n", + "pl.rcParams['ytick.major.size'] = 8\n", + "pl.rcParams['ytick.minor.size'] = 4\n", + "pl.rcParams['ytick.major.pad' ] = 8\n", + "pl.rcParams['ytick.minor.pad' ] = 8\n", + "pl.rcParams['ytick.color' ] = 'k'\n", + "pl.rcParams['ytick.labelsize' ] = 'medium'\n", + "pl.rcParams['ytick.direction' ] = 'in'" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "def dydt_0(y, t0):\n", + " '''\n", + " '''\n", + " E_00, B_01 = y\n", + " dydt = [-B_01 * 2 * np.pi, E_00 * 2 * np.pi]\n", + " \n", + " return dydt\n", + "\n", + "def dydt_1(y, t0):\n", + " '''\n", + " '''\n", + " E_01, B_00 = y\n", + " dydt = [B_00 * 2 * np.pi, -E_01 * 2 * np.pi]\n", + " \n", + " return dydt" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "E_00_B_01_init = [1.0, 0.5]\n", + "E_01_B_00_init = [1.0, 0.2]\n", + "\n", + "t = np.arange(0., 2., params.delta_t)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "E_00_B_01 = odeint(dydt_0, E_00_B_01_init, t)\n", + "E_01_B_00 = odeint(dydt_1, E_01_B_00_init, t)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. 0.5 ]\n", + " [ 0.98972424 0.52004417]\n", + " [ 0.97904674 0.53987729]\n", + " ..., \n", + " [ 1.02600856 0.44419245]\n", + " [ 1.01685179 0.46477191]\n", + " [ 1.00728229 0.48516273]]\n" + ] + } + ], + "source": [ + "print(E_00_B_01)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.00406017954\n" + ] + } + ], + "source": [ + "print(params.delta_t * i * 5)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "9\n", + "10\n", + "11\n", + "12\n", + "13\n", + "14\n", + "15\n", + "16\n", + "17\n", + "18\n", + "19\n", + "20\n", + "21\n", + "22\n", + "23\n", + "24\n", + "25\n", + "26\n", + "27\n", + "28\n", + "29\n", + "30\n", + "31\n", + "32\n", + "33\n", + "34\n", + "35\n", + "36\n", + "37\n", + "38\n", + "39\n", + "40\n", + "41\n", + "42\n", + "43\n", + "44\n", + "45\n", + "46\n", + "47\n", + 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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;31m# i = 20\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mE_z\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mE_00_B_01\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m5\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m 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\u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0melement_LGL\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mE_00_B_01\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m5\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0melement_LGL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mIndexError\u001b[0m: index 625 is out of bounds for axis 0 with size 624" + ] + } + ], + "source": [ + "for i in np.arange(126):\n", + "# i = 20\n", + " print(i)\n", + " E_z = E_00_B_01[5 * i][0] * np.sin(2 * np.pi * params.element_LGL) + E_01_B_00[5 * i][0] * np.cos(2 * np.pi * params.element_LGL)\n", + " B_y = E_01_B_00[5 * i][1] * np.sin(2 * np.pi * params.element_LGL) + E_00_B_01[5 * i][1] * np.cos(2 * np.pi * params.element_LGL)\n", + "\n", + " f, (ax1, ax2) = pl.subplots(2, sharex = True, sharey = True)\n", + "\n", + " h5py_data = h5py.File('../../results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(5 * i)) + '.hdf5', 'r')\n", + " E_z_LGL = (h5py_data['E_z'][:])\n", + " B_y_LGL = (h5py_data['B_y'][:])\n", + "\n", + " ax1.plot(params.element_LGL, E_z)\n", + " ax2.plot(params.element_LGL, B_y)\n", + "\n", + " ax1.plot(params.element_LGL, E_z_LGL, '.')\n", + " ax2.plot(params.element_LGL, B_y_LGL, '.')\n", + "\n", + "\n", + " pl.xlabel(r'$x$')\n", + " ax1.set_ylabel(r'$E_z$')\n", + " ax2.set_ylabel(r'$B_y$')\n", + " pl.xlim(-1, 1)\n", + " pl.ylim(-2, 2)\n", + " pl.title(r'$E_z$ Time = %.2f' % (i * 5 * params.delta_t))\n", + " f.savefig('../../results/1D_Wave_images_/%04d' %(i) + '.png')\n", + " pl.close('all')\n", + "\n", + "# pl.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/main.py b/main.py index f87445c..3c19ee3 100644 --- a/main.py +++ b/main.py @@ -30,4 +30,3 @@ u_init[:, :, 1] = B_y_init u_diff = wave_equation.time_evolution(u_init) - print(lagrange.L1_norm(u_diff)) diff --git a/post_processing.py b/post_processing.py index ae1ea11..3cc576c 100644 --- a/post_processing.py +++ b/post_processing.py @@ -55,18 +55,24 @@ file_count = len(files) print(file_count) - for i in trange(0, file_count): - fig = pl.figure() - h5py_data = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(20 * i)) + '.hdf5', 'r') - u_LGL = (h5py_data['u_i'][:]) - pl.plot(params.element_LGL, u_LGL) - pl.xlabel('x') - pl.ylabel('u') + + f, (ax1, ax2) = pl.subplots(2, sharex = True, sharey = True) + + h5py_data = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(5 * i)) + '.hdf5', 'r') + E_z_LGL = (h5py_data['E_z'][:]) + B_y_LGL = (h5py_data['B_y'][:]) + + ax1.plot(params.element_LGL, E_z_LGL) + ax2.plot(params.element_LGL, B_y_LGL) + + pl.xlabel(r'$x$') + ax1.set_ylabel(r'$E_z$') + ax2.set_ylabel(r'$B_y$') pl.xlim(-1, 1) pl.ylim(-2, 2) - pl.title('Time = %f' % (i * 20 * params.delta_t)) - fig.savefig('results/1D_Wave_images/%04d' %(i) + '.png') + pl.title(r'$E_z$ Time = %.2f' % (i * 5 * params.delta_t)) + f.savefig('results/1D_Wave_images/%04d' %(i) + '.png') pl.close('all') # Creating a movie with the images created. From fb8906325ec0ca4e7f55129a17ef79c8acca44ae Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 18:15:13 +0530 Subject: [PATCH 07/13] Minor cleanup, documentation checked --- README.md | 2 +- dg_maxwell/isoparam.py | 5 +- dg_maxwell/lagrange.py | 5 +- dg_maxwell/msh_parser.py | 5 +- dg_maxwell/params.py | 5 +- dg_maxwell/tests/convergence_tests.py | 5 +- dg_maxwell/tests/isoparam/test_isoparam.py | 5 +- .../tests/msh_parser/test_msh_parser.py | 5 +- dg_maxwell/tests/test_waveEqn.py | 63 +--- dg_maxwell/tests/utils/test_utils.py | 4 +- dg_maxwell/utils.py | 10 +- dg_maxwell/wave_equation.py | 334 +----------------- docs/conf.py | 4 +- main.py | 24 +- post_processing.py | 4 +- requirements.txt | 6 +- 16 files changed, 82 insertions(+), 404 deletions(-) diff --git a/README.md b/README.md index 6958889..787c56c 100644 --- a/README.md +++ b/README.md @@ -3,7 +3,7 @@ [![Build Status](https://travis-ci.org/QuazarTech/DG_Maxwell.svg?branch=master)](https://travis-ci.org/QuazarTech/DG_Maxwell) [![Codacy Badge](https://api.codacy.com/project/badge/Grade/e8733cdbf1454af0ac35ae5b2d017d9f)](https://www.codacy.com/app/aman2official/DG_Maxwell_2?utm_source=github.com&utm_medium=referral&utm_content=QuazarTech/DG_Maxwell&utm_campaign=Badge_Grade) [![Documentation Status](http://readthedocs.org/projects/dg-maxwell/badge/?version=latest)](http://dg-maxwell.readthedocs.io/en/latest/?badge=latest) - +[![Coverage Status](https://coveralls.io/repos/github/QuazarTech/DG_Maxwell/badge.svg?branch=master)](https://coveralls.io/github/QuazarTech/DG_Maxwell?branch=master) ``` _____ _____ __ __ _ _ | __ \ / ____| | \/ | | | | diff --git a/dg_maxwell/isoparam.py b/dg_maxwell/isoparam.py index 3d3c0ff..dc814c7 100644 --- a/dg_maxwell/isoparam.py +++ b/dg_maxwell/isoparam.py @@ -2,8 +2,9 @@ # -*- coding: utf-8 -*- import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import utils diff --git a/dg_maxwell/lagrange.py b/dg_maxwell/lagrange.py index 5acf673..809b8fa 100644 --- a/dg_maxwell/lagrange.py +++ b/dg_maxwell/lagrange.py @@ -4,8 +4,9 @@ import numpy as np from scipy import special as sp import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import utils from dg_maxwell import params diff --git a/dg_maxwell/msh_parser.py b/dg_maxwell/msh_parser.py index d10a80c..299722a 100644 --- a/dg_maxwell/msh_parser.py +++ b/dg_maxwell/msh_parser.py @@ -5,8 +5,9 @@ import matplotlib.lines as lines import gmshtranslator.gmshtranslator as gmsh import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import msh_parser from dg_maxwell import isoparam diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index c2d4c0e..ec9f933 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -3,8 +3,9 @@ import numpy as np import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import lagrange from dg_maxwell import utils diff --git a/dg_maxwell/tests/convergence_tests.py b/dg_maxwell/tests/convergence_tests.py index 45887e8..3f784ba 100644 --- a/dg_maxwell/tests/convergence_tests.py +++ b/dg_maxwell/tests/convergence_tests.py @@ -2,8 +2,9 @@ from dg_maxwell import wave_equation import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) def L1_norm(u): ''' diff --git a/dg_maxwell/tests/isoparam/test_isoparam.py b/dg_maxwell/tests/isoparam/test_isoparam.py index e750e68..37367a6 100644 --- a/dg_maxwell/tests/isoparam/test_isoparam.py +++ b/dg_maxwell/tests/isoparam/test_isoparam.py @@ -6,8 +6,9 @@ sys.path.insert(0, os.path.abspath('./')) import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) import numpy as np diff --git a/dg_maxwell/tests/msh_parser/test_msh_parser.py b/dg_maxwell/tests/msh_parser/test_msh_parser.py index a563f33..26c0e77 100644 --- a/dg_maxwell/tests/msh_parser/test_msh_parser.py +++ b/dg_maxwell/tests/msh_parser/test_msh_parser.py @@ -6,8 +6,9 @@ sys.path.insert(0, os.path.abspath('./')) import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) import numpy as np diff --git a/dg_maxwell/tests/test_waveEqn.py b/dg_maxwell/tests/test_waveEqn.py index ca33465..61000a5 100644 --- a/dg_maxwell/tests/test_waveEqn.py +++ b/dg_maxwell/tests/test_waveEqn.py @@ -7,8 +7,9 @@ import numpy as np import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import params from dg_maxwell import lagrange @@ -371,60 +372,7 @@ def test_volume_integral_flux(): ]))) - numerical_flux = wave_equation.volume_integral_flux(params.u[:, :, 0]) - assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) - -def test_volume_integral_flux_multiple_u_n(): - ''' - A test function to check the volume_integral_flux function in wave_equation - module by analytically calculated Gauss-Lobatto quadrature. - - Reference - --------- - The link to the sage worksheet where the calculations were caried out is - given below. - `https://goo.gl/5Mub8M` - ''' - threshold = 4e-9 - params.c = 1 - change_parameters(8, 10, 11, 'gaussian') - - referenceFluxIntegral = af.transpose(af.interop.np_to_af_array(np.array - ([ - [-0.002016634876668093, -0.000588597708116113, -0.0013016773719126333,\ - -0.002368387579324652, -0.003620502047659841, -0.004320197094090966, - -0.003445512010153811, 0.0176615086879261],\ - - [-0.018969769374, -0.00431252844519,-0.00882630935977,-0.0144355176966,\ - -0.019612124119, -0.0209837936827, -0.0154359890788, 0.102576031756], \ - - [-0.108222418798, -0.0179274222595, -0.0337807018822, -0.0492589052599,\ - -0.0588472807471, -0.0557970236273, -0.0374764132459, 0.361310165819],\ - - [-0.374448714304, -0.0399576371245, -0.0683852285846, -0.0869229749357,\ - -0.0884322503841, -0.0714664112839, -0.0422339853622, 0.771847201979], \ - - [-0.785754362849, -0.0396035640187, -0.0579313769517, -0.0569022801117,\ - -0.0392041960688, -0.0172295769141, -0.00337464521455, 1.00000000213],\ - - [-1.00000000213, 0.00337464521455, 0.0172295769141, 0.0392041960688,\ - 0.0569022801117, 0.0579313769517, 0.0396035640187, 0.785754362849],\ - - [-0.771847201979, 0.0422339853622, 0.0714664112839, 0.0884322503841, \ - 0.0869229749357, 0.0683852285846, 0.0399576371245, 0.374448714304],\ - - [-0.361310165819, 0.0374764132459, 0.0557970236273, 0.0588472807471,\ - 0.0492589052599, 0.0337807018822, 0.0179274222595, 0.108222418798], \ - - [-0.102576031756, 0.0154359890788, 0.0209837936827, 0.019612124119, \ - 0.0144355176966, 0.00882630935977, 0.00431252844519, 0.018969769374],\ - - [-0.0176615086879, 0.00344551201015 ,0.00432019709409, 0.00362050204766,\ - 0.00236838757932, 0.00130167737191, 0.000588597708116, 0.00201663487667]\ - - ]))) - - numerical_flux = wave_equation.volume_integral_flux_multiple_u_n( + numerical_flux = wave_equation.volume_integral_flux( params.u[:, :, 0]) assert (af.mean(af.abs(numerical_flux - referenceFluxIntegral)) < threshold) @@ -486,7 +434,8 @@ def test_b_vector(): u_n_A_matrix = af.blas.matmul(wave_equation.A_matrix(),\ params.u[:, :, 0]) - volume_integral_flux = wave_equation.volume_integral_flux(params.u[:, :, 0]) + volume_integral_flux = wave_equation.volume_integral_flux( + params.u[:, :, 0]) surface_term = test_surface_term() b_vector_analytical = u_n_A_matrix + (volume_integral_flux -\ (surface_term)) * params.delta_t diff --git a/dg_maxwell/tests/utils/test_utils.py b/dg_maxwell/tests/utils/test_utils.py index 07b0394..5184dab 100644 --- a/dg_maxwell/tests/utils/test_utils.py +++ b/dg_maxwell/tests/utils/test_utils.py @@ -8,8 +8,8 @@ from dg_maxwell import utils from dg_maxwell import lagrange -af.set_backend('opencl') -af.set_device(1) +af.set_backend('cpu') +af.set_device(0) def test_matmul_3D(): ''' diff --git a/dg_maxwell/utils.py b/dg_maxwell/utils.py index d66388a..1431eee 100644 --- a/dg_maxwell/utils.py +++ b/dg_maxwell/utils.py @@ -4,8 +4,9 @@ import numpy as np import matplotlib.lines as lines import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) def add(a, b): ''' @@ -187,6 +188,7 @@ def shape(array): def polyval_1d(polynomials, xi): ''' Finds the value of the polynomials at the given :math:`\\xi` coordinates. + Parameters ---------- polynomials : af.Array [number_of_polynomials N 1 1] @@ -197,6 +199,7 @@ def polyval_1d(polynomials, xi): xi : af.Array [N 1 1 1] :math:`\\xi` coordinates at which the :math:`i^{th}` Lagrange basis polynomial is to be evaluated. + Returns ------- af.Array [i.shape[0] xi.shape[0] 1 1] @@ -218,6 +221,7 @@ def poly1d_product(poly_a, poly_b): ''' Finds the product of two polynomials using the arrayfire convolve1 function. + Parameters ---------- poly_a : af.Array[N degree_a 1 1] @@ -234,12 +238,14 @@ def matmul_3D(a, b): ''' Finds the matrix multiplication of :math:`Q` pairs of matrices ``a`` and ``b``. + Parameters ---------- a : af.Array [M N Q 1] First set of :math:`Q` 2D arrays :math:`N \\neq 1` and :math:`M \\neq 1`. b : af.Array [N P Q 1] Second set of :math:`Q` 2D arrays :math:`P \\neq 1`. + Returns ------- matmul : af.Array [M P Q 1] diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 999ac61..8c015f9 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -4,8 +4,9 @@ import os import arrayfire as af -af.set_backend('opencl') -af.set_device(1) + +af.set_backend('cpu') +af.set_device(0) import numpy as np from matplotlib import pyplot as plt @@ -196,7 +197,10 @@ def flux_x(u): of numpy.poly1d polynomials. ''' + ## Normal flux #flux = params.c * u + + # Flux for solving 1D Maxwell's equations flux = u.copy() flux[:, :, 0] = -u[:, :, 1] @@ -205,21 +209,6 @@ def flux_x(u): return flux -def flux_maxwell(cons_var): - ''' - Fluxes for the :math:`(E_z, B_y)` mode in :math:`1D` Maxwell's equations. - - Parameters - ---------- - - cons_var : af.Array [N_Elements 2] - ''' - - E_z = cons_var[0] - B_y = cons_var[1] - - return (-B_y, E_z) - def volume_integral_flux(u_n): ''' @@ -241,99 +230,6 @@ def volume_integral_flux(u_n): Parameters ---------- - u : arrayfire.Array [N_LGL N_Elements 1 1] - Amplitude of the wave at the mapped LGL nodes of each element. - - Returns - ------- - - flux_integral : arrayfire.Array [N_LGL N_Elements 1 1] - Value of the volume integral flux. It contains the integral - of all N_LGL * N_Element integrands. - - ''' - # The coefficients of dLp / d\xi - diff_lag_coeff = params.dl_dxi_coeffs - - lobatto_nodes = params.lobatto_quadrature_nodes - Lobatto_weights = params.lobatto_weights_quadrature - - nodes_tile = af.transpose(af.tile(lobatto_nodes, 1, diff_lag_coeff.shape[1])) - power = af.flip(af.range(diff_lag_coeff.shape[1])) - power_tile = af.tile(power, 1, params.N_quad) - nodes_power = nodes_tile ** power_tile - weights_tile = af.transpose(af.tile(Lobatto_weights, 1, diff_lag_coeff.shape[1])) - nodes_weight = nodes_power * weights_tile - - dLp_dxi = af.matmul(diff_lag_coeff, nodes_weight) - - - # The first option to calculate the volume integral term, directly uses - # the Lobatto quadrature instead of using the integrate() function by - # passing the coefficients of the Lagrange interpolated polynomial. - if(params.volume_integral_scheme == 'lobatto_quadrature'\ - and params.N_quad == params.N_LGL): - - # Flux using u_n, reordered to 1 X N_LGL X N_Elements array. - F_u_n = af.reorder(flux_x(u_n), 2, 0, 1) - - # Multiplying with dLp / d\xi - integral_expansion = af.broadcast(utils.multiply,\ - dLp_dxi, F_u_n) - - # Using the quadrature rule. - flux_integral = af.sum(integral_expansion, 1) - flux_integral = af.reorder(flux_integral, 0, 2, 1) - - # Using the integrate() function to calculate the volume integral term - # by passing the Lagrange interpolated polynomial. - else: - #print('option3') - analytical_flux_coeffs = flux_x(lagrange.\ - lagrange_interpolation_u(u_n)) - - analytical_flux_coeffs = af.reorder(analytical_flux_coeffs, 1, 0, 2) - - dl_dxi_coefficients = af.reorder(params.dl_dxi_coeffs, 1, 0) - - # The product of polynomials is calculated using af.convolve1 - volume_int_coeffs = af.convolve1(dl_dxi_coefficients,\ - analytical_flux_coeffs,\ - conv_mode=af.CONV_MODE.EXPAND) - volume_int_coeffs = af.reorder(volume_int_coeffs, 1, 2, 0) - volume_int_coeffs = af.moddims(volume_int_coeffs,\ - params.N_LGL * params.N_Elements,\ - 2 * params.N_LGL - 2) - - - flux_integral = lagrange.integrate(volume_int_coeffs) - flux_integral = af.moddims(flux_integral, params.N_LGL, params.N_Elements) - - - return flux_integral - - - -def volume_integral_flux_multiple_u_n(u_n): - ''' - - Calculates the volume integral of flux in the wave equation. - - :math:`\\int_{-1}^1 f(u) \\frac{d L_p}{d\\xi} d\\xi` - - This will give N values of flux integral as p varies from 0 to N - 1. - - This integral is carried out using the analytical form of the integrand - obtained as a linear combination of Lagrange basis polynomials. - - This integrand is the used in the integrate() function. - - Calculation of volume integral flux using N_LGL Lobatto quadrature points - can be vectorized and is much faster. - - Parameters - ---------- - u : arrayfire.Array [N_LGL N_Elements M 1] Amplitude of the wave at the mapped LGL nodes of each element. This function can computer flux for :math:`M` :math:`u`. @@ -474,48 +370,6 @@ def lax_friedrichs_flux(u_n): -def analytical_u_LGL(t_n): - ''' - - Calculates the analytical u at the LGL points. - - Parameters - ---------- - - t_n : int - The timestep at which the analytical u is to be calculated. - - Returns - ------- - - u_t_n : arrayfire.Array [N_LGL N_Elements 1 1] - The value of u at the mapped LGL points in each element. - - ''' - - time = t_n * params.delta_t - - #u_t_n = af.sin(2 * np.pi * (params.element_LGL - params.c * time)) - - # Multiple waves test - E_00 = 1. - E_01 = 1. - - B_00 = 0.2 - B_01 = 0.5 - - E_z_t_n = E_00 * af.sin(2 * np.pi * (params.element_LGL - params.c * time))\ - + E_01 * af.cos(2 * np.pi * (params.element_LGL - params.c * time)) - - B_y_t_n = B_00 * af.sin(2 * np.pi * (params.element_LGL - params.c * time))\ - + B_01 * af.cos(2 * np.pi * (params.element_LGL - params.c * time)) - - u_t_n = B_y_t_n - - return u_t_n - - - def surface_term(u_n): ''' @@ -524,45 +378,6 @@ def surface_term(u_n): using the lax_friedrichs_flux function and lagrange_basis_value from params module. - Parameters - ---------- - u_n : arrayfire.Array [N_LGL N_Elements 1 1] - Amplitude of the wave at the mapped LGL nodes of each element. - - Returns - ------- - surface_term : arrayfire.Array [N_LGL N_Elements 1 1] - The surface term represented in the form of an array, - :math:`L_p (1) f_i - L_p (-1) f_{i - 1}`, where p varies - from zero to :math:`N_{LGL}` and i from zero to - :math:`N_{Elements}`. p varies along the rows and i along - columns. - - **See:** `PDF`_ describing the algorithm to obtain the surface term. - - .. _PDF: https://goo.gl/Nhhgzx - - ''' - - L_p_minus1 = params.lagrange_basis_value[:, 0] - L_p_1 = params.lagrange_basis_value[:, -1] - f_i = lax_friedrichs_flux(u_n) - f_iminus1 = af.shift(f_i, 0, 1) - surface_term = af.blas.matmul(L_p_1, f_i) - af.blas.matmul(L_p_minus1,\ - f_iminus1) - - return surface_term - - - -def surface_term_multiple_u(u_n): - ''' - - Calculates the surface term, - :math:`L_p(1) f_i - L_p(-1) f_{i - 1}` - using the lax_friedrichs_flux function and lagrange_basis_value - from params module. - Parameters ---------- u_n : arrayfire.Array [N_LGL N_Elements M 1] @@ -623,15 +438,14 @@ def b_vector(u_n): .. _Report: https://goo.gl/sNsXXK ''' - volume_integral = volume_integral_flux_multiple_u_n(u_n) - Surface_term = surface_term_multiple_u(u_n) + volume_integral = volume_integral_flux(u_n) + Surface_term = surface_term(u_n) b_vector_array = (volume_integral - Surface_term) return b_vector_array - def RK4_timestepping(A_inverse, u, delta_t): ''' @@ -639,44 +453,9 @@ def RK4_timestepping(A_inverse, u, delta_t): Parameters ---------- - A_inverse : arrayfire.Array[N_LGL N_LGL 1 1] - The inverse of the A matrix which was calculated - using A_matrix() function. - - u : arrayfire.Array[N_LGL N_Elements 1 1] - u at the mapped LGL points - - delta_t : float64 - The time-step by which u is to be evolved. - - Returns - ------- - delta_u : arrayfire.Array [N_LGL N_Elements 1 1] - The change in u at the mapped LGL points. - - ''' - - k1 = af.matmul(A_inverse, b_vector(u)) - k2 = af.matmul(A_inverse, b_vector(u + k1 * delta_t / 2)) - k3 = af.matmul(A_inverse, b_vector(u + k2 * delta_t / 2)) - k4 = af.matmul(A_inverse, b_vector(u + k3 * delta_t)) - - delta_u = delta_t * (k1 + 2 * k2 + 2 * k3 + k4) / 6 - - return delta_u - - - -def RK4_timestepping_multiple_u(A_inverse, u, delta_t): - ''' - - Implementing the Runge-Kutta (RK4) method to evolve the wave. - - Parameters - ---------- - A_inverse : arrayfire.Array[N_LGL N_LGL 1 1] - The inverse of the A matrix which was calculated - using A_matrix() function. + A_inverse : arrayfire.Array[N_LGL N_LGL M 1] + The inverse of the A matrix for :math:`M` differential + equations. u : arrayfire.Array[N_LGL N_Elements M 1] u at the mapped LGL points @@ -700,70 +479,12 @@ def RK4_timestepping_multiple_u(A_inverse, u, delta_t): return delta_u -def RK6_timestepping(A_inverse, u, delta_t): - ''' - - Implementing the Runge-Kutta (RK4) method to evolve the wave. - - Parameters - ---------- - A_inverse : arrayfire.Array[N_LGL N_LGL 1 1] - The inverse of the A matrix which was calculated - using A_matrix() function. - - u : arrayfire.Array[N_LGL N_Elements 1 1] - u at the mapped LGL points - - delta_t : float64 - The time-step by which u is to be evolved. - - Returns - ------- - delta_u : arrayfire.Array [N_LGL N_Elements 1 1] - The change in u at the mapped LGL points. - - ''' - - k1 = af.matmul(A_inverse, b_vector(u )) - k2 = af.matmul(A_inverse, b_vector(u + 0.25 * k1 * delta_t)) - k3 = af.matmul(A_inverse, b_vector(u + (3 / 32)\ - * (k1 \ - + 3 * k2)\ - * delta_t, )) - k4 = af.matmul(A_inverse, b_vector(u + (12 / 2197)\ - * (161 * k1\ - - 600 * k2 \ - + 608 * k3)\ - * delta_t, )) - k5 = af.matmul(A_inverse, b_vector(u + (1 / 4104)\ - * (8341 * k1\ - - 32832 * k2\ - + 29440 * k3\ - - 845 * k4)\ - * delta_t, )) - k6 = af.matmul(A_inverse, b_vector(u + (-(8/27) * k1\ - + 2 * k2\ - - (3544 / 2565) * k3\ - + (1859 / 4104) * k4\ - - (11 / 40) * k5)\ - * delta_t, )) - - delta_u = delta_t * 1 / 5 * ( (16 / 27) * k1\ - + (6656 / 2565) * k3\ - + (28561 / 11286) * k4\ - - (9 / 10) * k5\ - + (2 / 11) * k6\ - ) - - return delta_u - - - def time_evolution(u = None): ''' - Solves the wave equation - :math: `u^{t_n + 1} = b(t_n) \\times A` + + ..math: u^{t_n + 1} = b(t_n) \\times A + iterated over time.shape[0] time steps t_n Second order time stepping is used. @@ -775,11 +496,7 @@ def time_evolution(u = None): Returns ------- - - u_diff : arrayfire.Array [N_LGL N_Elements 1 1] - The absolute of the difference between the numerical - and analytical value of u at the LGL points. - + None ''' # Creating a folder to store hdf5 files. If it doesn't exist. @@ -791,7 +508,6 @@ def time_evolution(u = None): element_LGL = params.element_LGL delta_t = params.delta_t - #u = params.u_init shape_u_n = utils.shape(u) time = params.time A_inverse = af.tile(af.inverse(A_matrix()), @@ -804,7 +520,8 @@ def time_evolution(u = None): # Storing u at timesteps which are multiples of 100. if (t_n % 5) == 0: - h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') + h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' \ + %(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') Ez_dset = h5file.create_dataset('E_z', data = u[:, :, 0], dtype = 'd') By_dset = h5file.create_dataset('B_y', data = u[:, :, 1], @@ -813,23 +530,8 @@ def time_evolution(u = None): Ez_dset[:, :] = u[:, :, 0] By_dset[:, :] = u[:, :, 1] - # # Implementing second order time-stepping. - # u_n_plus_half = u + af.matmul(A_inverse, b_vector(u))\ - # * delta_t / 2 - - # u += af.matmul(A_inverse, b_vector(u_n_plus_half))\ - # * delta_t # Implementing RK 4 scheme - u += RK4_timestepping_multiple_u(A_inverse, u, delta_t) - - # Implementing RK 6 scheme - #u += RK6_timestepping(A_inverse, u, delta_t) - - u_analytical = analytical_u_LGL(t_n + 1) - - #u_diff = af.abs(u[:, :, 1] - u_analytical) - + u += RK4_timestepping(A_inverse, u, delta_t) - #return u_diff diff --git a/docs/conf.py b/docs/conf.py index 51eec9e..90a253e 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -31,7 +31,7 @@ def __getattr__(cls, name): MOCK_MODULES = ['gmshtranslator', 'gmshtranslator.gmshtranslator', 'arrayfire', 'lagrange', 'scipy', 'numpy', 'matplotlib', 'matplotlib.lines', - 'dg_maxwell.params', 'tqdm'] + 'dg_maxwell.params', 'tqdm', 'h5py'] sys.modules.update((mod_name, Mock()) for mod_name in MOCK_MODULES) # -- General configuration ------------------------------------------------ @@ -149,7 +149,7 @@ def __getattr__(cls, name): # The name of an image file (relative to this directory) to place at the top # of the sidebar. -html_logo = "docs/quazar_logo.png" +html_logo = "quazar_logo.png" # The name of an image file (relative to this directory) to use as a favicon of # the docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 diff --git a/main.py b/main.py index 3c19ee3..e4b8d0e 100644 --- a/main.py +++ b/main.py @@ -2,9 +2,9 @@ import numpy as np import arrayfire as af -af.set_backend('opencl') -af.set_device(1) -af.info() + +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import params from dg_maxwell import wave_equation @@ -12,7 +12,8 @@ if __name__ == '__main__': # 1. Set the initial conditions - + + ## 1. Sin E_00 = 1. E_01 = 1. @@ -24,7 +25,20 @@ B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \ + B_01 * af.cos(2 * np.pi * params.element_LGL) - + + ### 2. Gaussian + #E_0 = 1. + #B_0 = 1. + + #sigma = 0.1 + + #E_z_init = E_0 * np.e**(-(params.element_LGL)**2 / sigma**2) + #B_y_init = B_0 * np.e**(-(params.element_LGL)**2 / sigma**2) + + + ################################################################ + ######################## SET u_init ############################ + ################################################################ u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2) u_init[:, :, 0] = E_z_init u_init[:, :, 1] = B_y_init diff --git a/post_processing.py b/post_processing.py index 3cc576c..e8001a6 100644 --- a/post_processing.py +++ b/post_processing.py @@ -39,8 +39,6 @@ pl.rcParams['ytick.direction' ] = 'in' - - # Creating a folder to store hdf5 files. If it doesn't exist. results_directory = 'results/1D_Wave_images' @@ -71,7 +69,7 @@ ax2.set_ylabel(r'$B_y$') pl.xlim(-1, 1) pl.ylim(-2, 2) - pl.title(r'$E_z$ Time = %.2f' % (i * 5 * params.delta_t)) + pl.title(r'Time = %.2f' % (i * 5 * params.delta_t)) f.savefig('results/1D_Wave_images/%04d' %(i) + '.png') pl.close('all') diff --git a/requirements.txt b/requirements.txt index f7b66f7..94b1672 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,9 +1,11 @@ pytest +pytest-cov +coveralls +python-coveralls arrayfire numpy matplotlib tqdm scipy gmshtranslator -h5py - +h5py \ No newline at end of file From 202e4fcbb7d56258a5736ac531e32ba5b9ef3a0b Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 18:21:23 +0530 Subject: [PATCH 08/13] flux_x changed to c * u --- dg_maxwell/wave_equation.py | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 8c015f9..28df7e4 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -197,14 +197,14 @@ def flux_x(u): of numpy.poly1d polynomials. ''' - ## Normal flux - #flux = params.c * u + # Normal flux + flux = params.c * u - # Flux for solving 1D Maxwell's equations - flux = u.copy() + ## Flux for solving 1D Maxwell's equations + #flux = u.copy() - flux[:, :, 0] = -u[:, :, 1] - flux[:, :, 1] = -u[:, :, 0] + #flux[:, :, 0] = -u[:, :, 1] + #flux[:, :, 1] = -u[:, :, 0] return flux From 9305410a250a290a597bd3ac9a0ed3150603bcba Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 18:48:42 +0530 Subject: [PATCH 09/13] Added Maxwell's equations result git for sin --- .gifs/maxwell_equation_1D_sin_init.gif | Bin 0 -> 884596 bytes README.md | 8 ++++++++ post_processing.py | 4 ++-- 3 files changed, 10 insertions(+), 2 deletions(-) create mode 100644 .gifs/maxwell_equation_1D_sin_init.gif diff --git a/.gifs/maxwell_equation_1D_sin_init.gif b/.gifs/maxwell_equation_1D_sin_init.gif new file mode 100644 index 0000000000000000000000000000000000000000..a36791b57ceec3fd1341a6be59897f519132e785 GIT binary patch literal 884596 zcmc%QS5Q;&+vxlBMxrTnETMM|9l;W+6iZM6u?7^RsR2b0Q4^$t8k%$ny<@1-1*F%| zn@B)K1gQc7DjfXp{qCDR@5R|O`8;cz%H zF)?LjWqp19OP4O$+1cH_d)Lj)&C}C!SYBa7P5tHNvtc(bMc%#=f7dqM>p_Z}bKzC; z$J0iiE}2i9r*N-bpR&32_3`6R9uJ#LPikdoDJCmwB`KcHJ8e~BWnX3Q^4{ff?%Br; zk85hBcKr^nF@$%6#CKlF??!0sgdTlgcci{St*-uPe!!F5;)}cShP&w&yUFKw^X+!a z+;$6{TUt+dc3mDC^62foBmTHl{#p59_mZ^RuO>Ze;~zA{+^`&dtqDOG~S&swyrnexDpS>*qfo6H}iS zyIcLDDLbvV>Rne^;X-=)N<~F|V2pp8e{64TM0Z5yaAwIwNzGKv*tp-PPZ8ZM;k)(0 zyKS-Dskp)V+TD?|zkNBMKc{}5tN6r?$?@-a7t>$J><)Z499lhAn>zf(yZKvi`%FOl zY;FRzB@Pa^XKT&O5b4P*Rl55#_{>d-ua)cGhavMHwNZ^jV~^JT5eig9h+Sp z__^_M?N`_0&&9>X*{@$#=jXS-f1BT!|FZgJckRd4#_W$TKfnE0-}>_N*N=_a_06@l zwcl$$e{TQ$v%U6nZR^k4_WJKXySuypIRXFw{1V-Q0DyZ3AiB$Q&fwBTJspaH@(~jF z-!6rJ$Mx?r0U&k&*~kM%Y*zgX1VQdvD?9mvKUUl%-l#C8DOga&@ndUYYRhY)UeE#K zqO`VfnTt8s+KSRUqDZ&eegSZ8gQdt*Zh3 zo%>o<#-941{jF9qtNbgSL1hbiDUgcD?E?zppE@fZm^RQpg9v(?U!*&2NIb_+kkr(M zK-Zrno~# zOPyWccTlbJbw|`XbD$u-y4sp2F9yHE0uJ3cxmo`6-TY+FP3o`qNrrVDdCN?Xe)S43 zi2`gl=be18cGf+~?XS7L=-pjgey;n#wL7e<2wuQ78s-8-M6KwU|JW_*43DW`Qbwex zpvb;2Q;Zl)G{+ORHhb&!0sI%ymoUs$La35dcG?A%AsNog$Agx`1~63_LDG!5(B&If zE{KnWQT;~4`C$Mmz_J-fs*_I1l5O?`(4d9@*a)=q{%vcYJGU;+8g(T?fO0b|AAZN# zCtvM-!tML&3(^g`N_>?rM+>S%g)Nknajy5o14qs zVK>Xo=amdO&Kug;GYpvTHiEKcFkJ79W#IiEH}$9Rj&;>E!Aw!U)n6(Wg18fa7tCjl7o5D@}rT@>ZG;Jo&w-I$G+6Z6qFbay5{+b^3}k zG~H{p16Ofo`~etEtYd@P&_BC*zIP_|9EVRR10*dGB^;x}H3@x2KRX{jIKIAJG)_2?o-lzrU<`>1fLvo18p=G(9D8JKCSCk%(v&yMSb5;g2Oh;}-mpfT zwuDY_enWg=Irv%{E{HThCZJ^<)25oHZ^V1geRWbw2*GFHX*i?T#;e?j^*yjZmvmi~ z1C=dNkvJo~|2WfdJr(qJsP{wWzDoTPi9)dG$6Qp++V@irg9I?~y|tO2GQU1ho{?92 zW>9T!t$S!L_=doYKq$4m9$tnu|I0~HIrD@3TtvwLMO_ZMm|YJ9e>6J6n;c+EcVwJ% zu~KEyAUC`q`z2?=*|GJ$@Xc=V2u;Y5lhB5Yv=DwhBkw6q8x$`GAiR^T1%=7~3cV)L zfLkk$^EEO=h~4&4gO1E#m?7C|$$-)pdB=17eJ*)g}UB zOT{Gd3!ik|i}Z&pFO16@Lz!seI7eUG6i4mtbkA1Xh|%213b+Aj4F6lq*< zs}~Xq5;h77XNLr;Vi}D_e;eK;t95MYn*nCWk0EhFkee8UWh z=qbYKnFdNf9mHq2aXx==O~OltA&-&_&;c~PZkHM0O`&7M_BCbg|Na4)B`9SG@eVjy z*d%&fM#_{7OfkZkSRC|*^9hQdDMIL~`spI|$!f-NH1D7Ga=rJ;1|?PLz{BB}f)5i@ zWkM;9RyP}wQfs=RSN|GQ58_`4%E-pP(`*;##H8I&wH7#0^?g_(F3iIbZwNh+WtL?e zD5&%yIrM4nDTDbi>v%xADHuoFUNUhyfhiE zPM5aZ+7cIqo!inEZ2W2ILRVzWJP&w7RZEd=WFI8P%x3*0*32Up+t5FuxP zOTKkjSjK^$Z$%j8rap_zJ6^{67dl|jt{ETUf&w9(nas@1j@>F$%MqNIHh8> z$_|QZnKmvm&7Fx{L!rid;k;;t0|#Wpb`YcH%D?=K;-~dpa`Jw^aCr&${j382G4SBn z=9{{Du%v*=<%_iv6zBS>lg3V+Ck}aZ^3_U;19YaJr#w(%=vjo;w7K;}#Nbr;QhbcNn9NVs!}g${CT=9juoupeRVlib=_{V*A3 z<3Zl1=>mh2>aw&MAn8SaaM$VQx}wi9^(YaVn_BYoKf^Na7sOO>bZKk4s15^d{pjJ| zg8(6WR|BOg${-lguSj|;CZj~?&y@-pp{@t8vv>{-49a>UA#+)!6`#ume))!%laamK z@=R{UTS?|c@~;zWt@sTMke(4Piv+|N$=0!<%~5zZ6|5uU<9^Xc!TMqBJA67DFz7Bz z}3Vvut!frO zz1jTQBpFpL2(o{N?WUk?DZu)XpmZ?-O91S?C6>cMxlzFitPo9|P~|&2qK!0^YB`eH=5v?+vI&o7ErZm_AjgU~3Uu&u(yQYxk$!I?kLyG^8$HlcIpyHMS#zzBc*Xa#<_4fokN zaVi`CwSrdaqCf@M{gF^QsG0e1R^h`5~O*5%XJ2RGc zZaa-4C)XX5Xf~HNku9KcCH;!Dod5px!WG1=iZ*~qEv_$!QPB!MNIli{DOZHUMK2e{dQK5mRGN^cZXKK z`lWoZNB)SM+s8RV+gScST*3HS{VM5IbKOA3AX4D107C8=y1UMvD%JUR3_W7i-t;O!|pH*_i+J7n6ON0RBRtlED3s! z3cbSPrV@pYrfF%>ASUdxWb<*Po*bseVA zZtVi0aWqI5V5S*Wy^T_(fk^Z#rg#kg0HV0AUcL~`q#=U2S4Xc zs5yLv{K`nwQ6kn+0X9T{`imOql$;CzfVxYgkvEL)_Y%343h|XP5&@; z<~oISGtaYyM@gYg4E79!b9*Bdjv_SE;nGC#fij^64uWvtNq{IusRRKG5p1L)&k&(b zWreGG*bfcTgem(`v_qH_fkVG$>@4_!0z0t`z3au{q$4ciclcWZ3>92W3`VkDLt2&OnQ%(tg zau^B}GKMz`5Hj3)xSWMR`L?U$c#g3_Zh)x$^1N37cc8?(FqV)$?7$>)5NwT7rh)9q ztvY5X0j{rC&A|#b!XJRVeUOk(11nJBj+keUYOpCR=&V#Pc?HEf4(9$Kbl1TMB%m{; z_Gk*a#p{DE5c7-*R_DU6o*gwVy#HH{Dcd@!6iI zI>*uz;IeekQQ}KAQOw=tVOz?8j}1@I4h?aW^HO;QerIB!V0&a$j`ukcBmw|EU_T}? 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insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 57ef1e3..8c752fc 100644 --- a/README.md +++ b/README.md @@ -101,6 +101,6 @@ $ pytest The movie will be created automatically and stored in `results` folder. ## Maintainers -- Aman Abhishek Tiwari - ![aman@quazartech.com](aman@quazartech.com) -- Balavarun P - ![f2013462@pilani.bits-pilani.ac.in](f2013462@pilani.bits-pilani.ac.in) -- Manichandra Morumpudi - ![mani@quazartech.com](mani@quazartech.com) +- Aman Abhishek Tiwari - [aman@quazartech.com](aman@quazartech.com) +- Balavarun P - [f2013462@pilani.bits-pilani.ac.in](f2013462@pilani.bits-pilani.ac.in) +- Manichandra Morumpudi - [mani@quazartech.com](mani@quazartech.com) From 8cf107caefff58d53c13fe348f01bc218072c1de Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 19:03:13 +0530 Subject: [PATCH 11/13] Minor changes --- .travis.yml | 4 +++- .../maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb | 7 +++++++ examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb | 7 +++++++ .../advec_1d_multiple_u_surface_term.ipynb | 7 +++++++ .../advec_1d_multiple_u_volume_term.ipynb | 7 +++++++ examples/maxwells_equations/analytical_solution.ipynb | 7 +++++++ post_processing.py | 2 +- 7 files changed, 39 insertions(+), 2 deletions(-) diff --git a/.travis.yml b/.travis.yml index c10b6b0..b11ca3c 100644 --- a/.travis.yml +++ b/.travis.yml @@ -54,4 +54,6 @@ install: script: - python -c "import dg_maxwell" - - pytest --verbose -r P --color=yes + - pytest --verbose -r P --color=yes --cov dg_maxwell +after_success: + - coveralls diff --git a/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb index 4c687e3..7df1429 100644 --- a/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb +++ b/examples/maxwells_equations/advec_1d_multiple_u_LF_flux.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Developmental file for modifying the 1D advection solver to work for multiple wave equations" + ] + }, { "cell_type": "code", "execution_count": 1, diff --git a/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb index 3aeab5f..b69ca16 100644 --- a/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb +++ b/examples/maxwells_equations/advec_1d_multiple_u_RK4.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Developmental file for modifying the 1D advection solver to work for multiple wave equations" + ] + }, { "cell_type": "code", "execution_count": 1, diff --git a/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb index 0f700c6..530a44b 100644 --- a/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb +++ b/examples/maxwells_equations/advec_1d_multiple_u_surface_term.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Developmental file for modifying the 1D advection solver to work for multiple wave equations" + ] + }, { "cell_type": "code", "execution_count": 1, diff --git a/examples/maxwells_equations/advec_1d_multiple_u_volume_term.ipynb b/examples/maxwells_equations/advec_1d_multiple_u_volume_term.ipynb index d541bb3..c5745ba 100644 --- a/examples/maxwells_equations/advec_1d_multiple_u_volume_term.ipynb +++ b/examples/maxwells_equations/advec_1d_multiple_u_volume_term.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Developmental file for modifying the 1D advection solver to work for multiple wave equations" + ] + }, { "cell_type": "code", "execution_count": 1, diff --git a/examples/maxwells_equations/analytical_solution.ipynb b/examples/maxwells_equations/analytical_solution.ipynb index 5c46b31..b5b28bc 100644 --- a/examples/maxwells_equations/analytical_solution.ipynb +++ b/examples/maxwells_equations/analytical_solution.ipynb @@ -1,5 +1,12 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# This is the developmental file for solving the Maxwell's Equation semi-analytically" + ] + }, { "cell_type": "code", "execution_count": 25, diff --git a/post_processing.py b/post_processing.py index 789a904..51de378 100644 --- a/post_processing.py +++ b/post_processing.py @@ -70,7 +70,7 @@ pl.xlim(-1, 1) pl.ylim(-2, 2) pl.suptitle(r'Time = %.2f' % (i * 5 * params.delta_t)) - f.savefig('results/1D_Wave_images/%04d' %(i) + '.png', dpi = 50) + f.savefig('results/1D_Wave_images/%04d' %(i) + '.png', dpi = 200) pl.close('all') # Creating a movie with the images created. From edcdafa13e52763c3bd86b8c5d126810bcdfbb3b Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 19:24:50 +0530 Subject: [PATCH 12/13] Code ready to be merged. --- dg_maxwell/params.py | 16 -------------- dg_maxwell/wave_equation.py | 30 +++++++++++++++---------- main.py | 24 ++++++++++---------- post_processing.py | 44 +++++++++++++++++++++++++------------ 4 files changed, 61 insertions(+), 53 deletions(-) diff --git a/dg_maxwell/params.py b/dg_maxwell/params.py index ec9f933..322e745 100644 --- a/dg_maxwell/params.py +++ b/dg_maxwell/params.py @@ -116,22 +116,6 @@ # Initializing the amplitudes. Change u_init to required initial conditions. if (wave=='sin'): - #E_00 = 1. - #E_01 = 1. - - #B_00 = 0.2 - #B_01 = 0.5 - - #E_z_init = E_00 * af.sin(2 * np.pi * element_LGL) \ - #+ E_01 * af.cos(2 * np.pi * element_LGL) - - #B_y_init = B_00 * af.sin(2 * np.pi * element_LGL) \ - #+ B_01 * af.cos(2 * np.pi * element_LGL) - - #u_init = af.constant(0., d0 = N_LGL, d1 = N_Elements, - #d2 = 2, dtype = af.Dtype.f64) - #u_init[:, :, 0] = E_z_init - #u_init[:, :, 1] = B_y_init u_init = af.sin(2 * np.pi * element_LGL) if (wave=='gaussian'): diff --git a/dg_maxwell/wave_equation.py b/dg_maxwell/wave_equation.py index 28df7e4..8de0efa 100644 --- a/dg_maxwell/wave_equation.py +++ b/dg_maxwell/wave_equation.py @@ -517,18 +517,24 @@ def time_evolution(u = None): element_boundaries = af.np_to_af_array(params.np_element_array) for t_n in trange(0, time.shape[0]): - - # Storing u at timesteps which are multiples of 100. - if (t_n % 5) == 0: - h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' \ - %(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') - Ez_dset = h5file.create_dataset('E_z', data = u[:, :, 0], - dtype = 'd') - By_dset = h5file.create_dataset('B_y', data = u[:, :, 1], - dtype = 'd') - - Ez_dset[:, :] = u[:, :, 0] - By_dset[:, :] = u[:, :, 1] + if (t_n % 20) == 0: + h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') + dset = h5file.create_dataset('u_i', data = u, dtype = 'd') + + dset[:, :] = u[:, :] + + # Code for solving 1D Maxwell's Equations + ## Storing u at timesteps which are multiples of 100. + #if (t_n % 5) == 0: + #h5file = h5py.File('results/hdf5_%02d/dump_timestep_%06d' \ + #%(int(params.N_LGL), int(t_n)) + '.hdf5', 'w') + #Ez_dset = h5file.create_dataset('E_z', data = u[:, :, 0], + #dtype = 'd') + #By_dset = h5file.create_dataset('B_y', data = u[:, :, 1], + #dtype = 'd') + + #Ez_dset[:, :] = u[:, :, 0] + #By_dset[:, :] = u[:, :, 1] # Implementing RK 4 scheme diff --git a/main.py b/main.py index e4b8d0e..978834b 100644 --- a/main.py +++ b/main.py @@ -14,17 +14,17 @@ # 1. Set the initial conditions ## 1. Sin - E_00 = 1. - E_01 = 1. + #E_00 = 1. + #E_01 = 1. - B_00 = 0.2 - B_01 = 0.5 + #B_00 = 0.2 + #B_01 = 0.5 - E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \ - + E_01 * af.cos(2 * np.pi * params.element_LGL) + #E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \ + #+ E_01 * af.cos(2 * np.pi * params.element_LGL) - B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \ - + B_01 * af.cos(2 * np.pi * params.element_LGL) + #B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \ + #+ B_01 * af.cos(2 * np.pi * params.element_LGL) ### 2. Gaussian #E_0 = 1. @@ -39,8 +39,10 @@ ################################################################ ######################## SET u_init ############################ ################################################################ - u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2) - u_init[:, :, 0] = E_z_init - u_init[:, :, 1] = B_y_init + #u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2) + #u_init[:, :, 0] = E_z_init + #u_init[:, :, 1] = B_y_init + + u_init = params.u_init u_diff = wave_equation.time_evolution(u_init) diff --git a/post_processing.py b/post_processing.py index 51de378..801a395 100644 --- a/post_processing.py +++ b/post_processing.py @@ -53,26 +53,42 @@ file_count = len(files) print(file_count) +# Example loop to run when solving for a single 1D wave equation. for i in trange(0, file_count): - f, (ax1, ax2) = pl.subplots(2, sharex = True, sharey = True) - - h5py_data = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(5 * i)) + '.hdf5', 'r') - E_z_LGL = (h5py_data['E_z'][:]) - B_y_LGL = (h5py_data['B_y'][:]) - - ax1.plot(params.element_LGL, E_z_LGL) - ax2.plot(params.element_LGL, B_y_LGL) - - pl.xlabel(r'$x$') - ax1.set_ylabel(r'$E_z$') - ax2.set_ylabel(r'$B_y$') + fig = pl.figure() + h5py_data = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(20 * i)) + '.hdf5', 'r') + u_LGL = (h5py_data['u_i'][:]) + pl.plot(params.element_LGL, u_LGL) + pl.xlabel('x') + pl.ylabel('u') pl.xlim(-1, 1) pl.ylim(-2, 2) - pl.suptitle(r'Time = %.2f' % (i * 5 * params.delta_t)) - f.savefig('results/1D_Wave_images/%04d' %(i) + '.png', dpi = 200) + pl.title('Time = %.2f' % (i * 20 * params.delta_t)) + fig.savefig('results/1D_Wave_images/%04d' %(i) + '.png', dpi = 100) pl.close('all') +# Example loop to run when solving for 1D Maxwell's equations. +#for i in trange(0, file_count): + + #f, (ax1, ax2) = pl.subplots(2, sharex = True, sharey = True) + + #h5py_data = h5py.File('results/hdf5_%02d/dump_timestep_%06d' %(int(params.N_LGL), int(5 * i)) + '.hdf5', 'r') + #E_z_LGL = (h5py_data['E_z'][:]) + #B_y_LGL = (h5py_data['B_y'][:]) + + #ax1.plot(params.element_LGL, E_z_LGL) + #ax2.plot(params.element_LGL, B_y_LGL) + + #pl.xlabel(r'$x$') + #ax1.set_ylabel(r'$E_z$') + #ax2.set_ylabel(r'$B_y$') + #pl.xlim(-1, 1) + #pl.ylim(-2, 2) + #pl.suptitle(r'Time = %.2f' % (i * 5 * params.delta_t)) + #f.savefig('results/1D_Wave_images/%04d' %(i) + '.png', dpi = 200) + #pl.close('all') + # Creating a movie with the images created. os.system("cd results/1D_Wave_images && ffmpeg -f image2 -i %04d.png -vcodec mpeg4\ -mbd rd -trellis 2 -cmp 2 -g 300 -pass 1 -r 25 -b 18000000 movie.mp4") From d796786401858cb73f8ce3063dd1c04189897366 Mon Sep 17 00:00:00 2001 From: AAT Date: Sun, 10 Dec 2017 20:07:17 +0530 Subject: [PATCH 13/13] Minor changes --- dg_maxwell/__init__.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/dg_maxwell/__init__.py b/dg_maxwell/__init__.py index d871a9c..635d747 100644 --- a/dg_maxwell/__init__.py +++ b/dg_maxwell/__init__.py @@ -2,7 +2,7 @@ # -*- coding: utf-8 -*- import arrayfire as af -af.set_backend('opencl') -af.set_device(1) +af.set_backend('cpu') +af.set_device(0) from dg_maxwell import params