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petsc_mhd2d_newton.py
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petsc_mhd2d_newton.py
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'''
Created on Mar 23, 2012
@author: Michael Kraus (michael.kraus@ipp.mpg.de)
'''
import sys, petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
import argparse
import time
from config import Config
from PETSc_MHD_DF import PETScSolver
from PETSc_MHD_DF_PC import PETScPreconditioner
from PETSc_MHD_Poisson import PETScPoissonSolver
from PETSc_MHD_DF_Function import PETScFunction
from PETSc_MHD_DF_Jacobian import PETScJacobian
class petscMHD2D(object):
'''
PETSc/Python Vlasov Poisson Solver in 1D.
'''
def __init__(self, cfgfile):
'''
Constructor
'''
# load run config file
cfg = Config(cfgfile)
# timestep setup
self.ht = cfg['grid']['ht'] # timestep size
self.nt = cfg['grid']['nt'] # number of timesteps
self.nsave = cfg['io']['nsave'] # save only every nsave'th timestep
# grid setup
nx = cfg['grid']['nx'] # number of points in x
ny = cfg['grid']['ny'] # number of points in y
Lx = cfg['grid']['Lx'] # spatial domain in x
x1 = cfg['grid']['x1'] #
x2 = cfg['grid']['x2'] #
Ly = cfg['grid']['Ly'] # spatial domain in y
y1 = cfg['grid']['y1'] #
y2 = cfg['grid']['y2'] #
if x1 != x2:
Lx = x2-x1
else:
x1 = 0.0
x2 = Lx
if y1 != y2:
Ly = y2-y1
else:
y1 = 0.0
y2 = Ly
self.hx = Lx / nx # gridstep size in x
self.hy = Ly / ny # gridstep size in y
self.time = PETSc.Vec().createMPI(1, PETSc.DECIDE, comm=PETSc.COMM_WORLD)
self.time.setName('t')
if PETSc.COMM_WORLD.getRank() == 0:
self.time.setValue(0, 0.0)
# set some PETSc options
OptDB = PETSc.Options()
OptDB.setValue('ksp_rtol', cfg['solver']['petsc_residual'])
# OptDB.setValue('ksp_max_it', 100)
OptDB.setValue('ksp_max_it', 200)
# OptDB.setValue('ksp_max_it', 1000)
# OptDB.setValue('ksp_max_it', 2000)
# OptDB.setValue('ksp_monitor', '')
# OptDB.setValue('log_info', '')
# OptDB.setValue('log_summary', '')
# create DA with single dof
self.da1 = PETSc.DA().create(dim=2, dof=1,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=1,
stencil_type='box')
# create DA (dof = 5 for Bx, By, Vx, Vy, P)
self.da4 = PETSc.DA().create(dim=2, dof=5,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=1,
stencil_type='box')
# create DA for x grid
self.dax = PETSc.DA().create(dim=1, dof=1,
sizes=[nx],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# create DA for y grid
self.day = PETSc.DA().create(dim=1, dof=1,
sizes=[ny],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# initialise grid
self.da1.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.da4.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.dax.setUniformCoordinates(xmin=x1, xmax=x2)
self.day.setUniformCoordinates(xmin=y1, xmax=y2)
# create solution and RHS vector
self.dx = self.da4.createGlobalVec()
self.x = self.da4.createGlobalVec()
self.b = self.da4.createGlobalVec()
self.Pb = self.da1.createGlobalVec()
self.localX = self.da4.createLocalVec()
# create global RK4 vectors
self.X1 = self.da4.createGlobalVec()
self.X2 = self.da4.createGlobalVec()
self.X3 = self.da4.createGlobalVec()
self.X4 = self.da4.createGlobalVec()
# create local RK4 vectors
self.localX1 = self.da4.createLocalVec()
self.localX2 = self.da4.createLocalVec()
self.localX3 = self.da4.createLocalVec()
self.localX4 = self.da4.createLocalVec()
# create vectors for magnetic and velocity field
self.Bx = self.da1.createGlobalVec()
self.By = self.da1.createGlobalVec()
self.Vx = self.da1.createGlobalVec()
self.Vy = self.da1.createGlobalVec()
self.P = self.da1.createGlobalVec()
# set variable names
self.x.setName('solver_x')
self.b.setName('solver_b')
self.Bx.setName('Bx')
self.By.setName('By')
self.Vx.setName('Vx')
self.Vy.setName('Vy')
self.P.setName('P')
# create Matrix object
self.petsc_matrix = PETScSolver (self.da1, self.da4, nx, ny, self.ht, self.hx, self.hy)
self.petsc_function = PETScFunction(self.da1, self.da4, nx, ny, self.ht, self.hx, self.hy)
self.petsc_jacobian = PETScJacobian(self.da1, self.da4, nx, ny, self.ht, self.hx, self.hy)
# create sparse matrix
self.J = PETSc.Mat().createPython([self.dx.getSizes(), self.b.getSizes()], comm=PETSc.COMM_WORLD)
self.J.setPythonContext(self.petsc_jacobian)
self.J.setUp()
# create linear solver and preconditioner
self.ksp = PETSc.KSP().create()
self.ksp.setFromOptions()
self.ksp.setOperators(self.J)
self.ksp.setType(cfg['solver']['petsc_ksp_type'])
self.ksp.setInitialGuessNonzero(True)
self.pc = self.ksp.getPC()
self.pc.setType(cfg['solver']['petsc_pc_type'])
# create Preconditioner matrix and solver
self.pc_mat = PETScPreconditioner(self.da1, self.da4, self.P, nx, ny, self.ht, self.hx, self.hy)
# create sparse matrix
self.pc_A = PETSc.Mat().createPython([self.x.getSizes(), self.b.getSizes()], comm=PETSc.COMM_WORLD)
self.pc_A.setPythonContext(self.pc_mat)
self.pc_A.setUp()
# create linear solver and preconditioner
self.pc_ksp = PETSc.KSP().create()
self.pc_ksp.setFromOptions()
self.pc_ksp.setOperators(self.pc_A)
self.pc_ksp.setType(cfg['solver']['petsc_ksp_type'])
self.pc_ksp.setInitialGuessNonzero(True)
self.pc_pc = self.pc_ksp.getPC()
self.pc_pc.setType('none')
# create Poisson matrix and solver
self.poisson_mat = PETScPoissonSolver(self.da1, self.da4, self.x,
nx, ny, self.ht, self.hx, self.hy)
self.poisson_A = PETSc.Mat().createPython([self.P.getSizes(), self.Pb.getSizes()], comm=PETSc.COMM_WORLD)
self.poisson_A.setPythonContext(self.poisson_mat)
self.poisson_A.setUp()
self.poisson_ksp = PETSc.KSP().create()
self.poisson_ksp.setFromOptions()
self.poisson_ksp.setOperators(self.poisson_A)
self.poisson_ksp.setType(cfg['solver']['petsc_ksp_type'])
# self.poisson_ksp.setInitialGuessNonzero(True)
self.poisson_pc = self.poisson_ksp.getPC()
self.poisson_pc.setType('none')
# create Arakawa solver object
# self.mhd_rk4 = PETScRK4(self.da4, nx, ny, self.ht, self.hx, self.hy)
# set initial data
(xs, xe), (ys, ye) = self.da1.getRanges()
coords = self.da1.getCoordinateDA().getVecArray(self.da1.getCoordinates())
# print
# print(self.hx)
# print(coords[1,0][0] - coords[0,0][0])
# print
# print(self.hy)
# print(coords[0,1][1] - coords[0,0][1])
# print
# print(Lx)
# print(coords[-1,0][0]+self.hx)
# print
# print(Ly)
# print(coords[0,-1][1]+self.hy)
# print
x_arr = self.da4.getVecArray(self.x)
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
# P_arr = self.da1.getVecArray(self.P)
if cfg['initial_data']['magnetic_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['magnetic_python'], globals(), locals(), ['magnetic_x', 'magnetic_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Bx_arr[i,j] = init_data.magnetic_x(coords[i,j][0], coords[i,j][1], Lx, Ly)
By_arr[i,j] = init_data.magnetic_y(coords[i,j][0], coords[i,j][1], Lx, Ly)
else:
Bx_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
By_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
if cfg['initial_data']['velocity_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['velocity_python'], globals(), locals(), ['velocity_x', 'velocity_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Vx_arr[i,j] = init_data.velocity_x(coords[i,j][0], coords[i,j][1], Lx, Ly)
Vy_arr[i,j] = init_data.velocity_y(coords[i,j][0], coords[i,j][1], Lx, Ly)
else:
Vx_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
Vy_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
# if cfg['initial_data']['pressure_python'] != None:
# init_data = __import__("runs." + cfg['initial_data']['pressure_python'], globals(), locals(), ['pressure', ''], 0)
#
# for i in range(xs, xe):
# for j in range(ys, ye):
# P_arr[i,j] = init_data.pressure(coords[i,j][0], coords[i,j][1], Lx, Ly) #+ 0.5 * (Bx_arr[i,j]**2 + By_arr[i,j]**2)
# copy distribution function to solution vector
x_arr[xs:xe, ys:ye, 0] = Bx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = By_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Vx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = Vy_arr[xs:xe, ys:ye]
self.petsc_matrix.formRHSPoisson(self.Pb, self.x)
self.poisson_ksp.solve(self.Pb, self.P)
x_arr = self.da4.getVecArray(self.x)
P_arr = self.da1.getVecArray(self.P)
x_arr[xs:xe, ys:ye, 4] = P_arr [xs:xe, ys:ye]
# update solution history
self.petsc_matrix.update_history(self.x)
self.petsc_function.update_history(self.x)
self.petsc_jacobian.update_history(self.x)
# create HDF5 output file
self.hdf5_viewer = PETSc.Viewer().createHDF5(cfg['io']['hdf5_output'],
mode=PETSc.Viewer.Mode.WRITE,
comm=PETSc.COMM_WORLD)
self.hdf5_viewer.HDF5PushGroup("/")
# write grid data to hdf5 file
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
coords_x.setName('x')
coords_y.setName('y')
self.hdf5_viewer(coords_x)
self.hdf5_viewer(coords_y)
# write initial data to hdf5 file
self.hdf5_viewer.HDF5SetTimestep(0)
self.hdf5_viewer(self.time)
# self.hdf5_viewer(self.x)
# self.hdf5_viewer(self.b)
self.hdf5_viewer(self.Bx)
self.hdf5_viewer(self.By)
self.hdf5_viewer(self.Vx)
self.hdf5_viewer(self.Vy)
self.hdf5_viewer(self.P)
def __del__(self):
# if self.hdf5_viewer != None:
# del self.hdf5_viewer
pass
def run(self):
(xs, xe), (ys, ye) = self.da4.getRanges()
for itime in range(1, self.nt+1):
if PETSc.COMM_WORLD.getRank() == 0:
localtime = time.asctime( time.localtime(time.time()) )
print("\nit = %4d, t = %10.4f, %s" % (itime, self.ht*itime, localtime) )
self.time.setValue(0, self.ht*itime)
# calculate initial guess
self.calculate_initial_guess()
# update previous iteration
self.petsc_jacobian.update_previous(self.x)
# build RHS and calculate norm
self.petsc_function.matrix_mult(self.x, self.b)
norm0 = self.b.norm()
self.b.scale(-1.)
# solve
self.dx.set(0.)
self.ksp.solve(self.b, self.dx)
# add to solution vector
self.x.axpy(1., self.dx)
# calculate function and norm
self.petsc_function.matrix_mult(self.x, self.b)
norm1 = self.b.norm()
# update history
self.petsc_function.update_history(self.x)
self.petsc_jacobian.update_history(self.x)
# copy solution to B and V vectors
x_arr = self.da4.getVecArray(self.x)
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
P_arr = self.da1.getVecArray(self.P)
Bx_arr[xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 0]
By_arr[xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 1]
Vx_arr[xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 2]
Vy_arr[xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 3]
P_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 4]
# save to hdf5 file
if itime % self.nsave == 0 or itime == self.nt + 1:
self.hdf5_viewer.HDF5SetTimestep(self.hdf5_viewer.HDF5GetTimestep() + 1)
self.hdf5_viewer(self.time)
# self.hdf5_viewer(self.x)
# self.hdf5_viewer(self.b)
self.hdf5_viewer(self.Bx)
self.hdf5_viewer(self.By)
self.hdf5_viewer(self.Vx)
self.hdf5_viewer(self.Vy)
self.hdf5_viewer(self.P)
if PETSc.COMM_WORLD.getRank() == 0:
print(" Solver: %5i iterations, residual = %24.16E " % (self.ksp.getIterationNumber(), self.ksp.getResidualNorm()) )
print(" Function Norm 0 = %24.16E" % (norm0) )
print(" Function Norm 1 = %24.16E" % (norm1) )
def calculate_initial_guess(self):
(xs, xe), (ys, ye) = self.da4.getRanges()
# explicit predictor for Bx, By, Vx, Vy
self.rk4(self.x)
# # calculate initial guess for total pressure
# self.petsc_matrix.formRHSPoisson(self.Pb, self.x)
# self.poisson_ksp.solve(self.Pb, self.P)
#
# P_arr = self.da1.getVecArray(self.P)
# x_arr = self.da4.getVecArray(self.x)
#
# x_arr[xs:xe, ys:ye, 4] = P_arr[xs:xe, ys:ye]
#
# if PETSc.COMM_WORLD.getRank() == 0:
# print(" Poisson: %5i iterations, residual = %24.16E " % (self.poisson_ksp.getIterationNumber(), self.poisson_ksp.getResidualNorm()) )
# calculate initial guess for total pressure
self.petsc_matrix.formRHSPoisson(self.Pb, self.x)
self.poisson_ksp.solve(self.Pb, self.P)
if PETSc.COMM_WORLD.getRank() == 0:
print(" Poisson: %5i iterations, residual = %24.16E " % (self.poisson_ksp.getIterationNumber(), self.poisson_ksp.getResidualNorm()) )
# precondition V and B
self.pc_mat.formRHS(self.b)
self.pc_ksp.solve(self.b, self.x)
if PETSc.COMM_WORLD.getRank() == 0:
print(" Precon : %5i iterations, residual = %24.16E " % (self.pc_ksp.getIterationNumber(), self.pc_ksp.getResidualNorm()) )
# precondition P
# self.petsc_matrix.formRHSPoisson(self.Pb, self.x)
# self.poisson_ksp.solve(self.Pb, self.P)
#
# if PETSc.COMM_WORLD.getRank() == 0:
# print(" Poisson: %5i iterations, residual = %24.16E " % (self.poisson_ksp.getIterationNumber(), self.poisson_ksp.getResidualNorm()) )
# copy pressure to solution vector
P_arr = self.da1.getVecArray(self.P)
x_arr = self.da4.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 4] = P_arr[xs:xe, ys:ye]
def rk4(self, X):
self.da4.globalToLocal(X, self.localX)
x = self.da4.getVecArray(self.localX)[...]
x1 = self.da4.getVecArray(self.X1)[...]
self.petsc_matrix.timestep(x, x1)
self.da4.globalToLocal(self.X1, self.localX1)
x1 = self.da4.getVecArray(self.localX1)[...]
x2 = self.da4.getVecArray(self.X2)[...]
self.petsc_matrix.timestep(x + 0.5 * self.ht * x1, x2)
self.da4.globalToLocal(self.X2, self.localX2)
x2 = self.da4.getVecArray(self.localX2)[...]
x3 = self.da4.getVecArray(self.X3)[...]
self.petsc_matrix.timestep(x + 0.5 * self.ht * x2, x3)
self.da4.globalToLocal(self.X3, self.localX3)
x3 = self.da4.getVecArray(self.localX3)[...]
x4 = self.da4.getVecArray(self.X4)[...]
self.petsc_matrix.timestep(x + 1.0 * self.ht * x3, x4)
x = self.da4.getVecArray(X)[...]
x1 = self.da4.getVecArray(self.X1)[...]
x2 = self.da4.getVecArray(self.X2)[...]
x3 = self.da4.getVecArray(self.X3)[...]
x4 = self.da4.getVecArray(self.X4)[...]
x[:,:,:] = x + self.ht * (x1 + 2.*x2 + 2.*x3 + x4) / 6.
if __name__ == '__main__':
parser = argparse.ArgumentParser(description='PETSc MHD Solver in 2D')
parser.add_argument('runfile', metavar='runconfig', type=str,
help='Run Configuration File')
args = parser.parse_args()
petscvp = petscMHD2D(args.runfile)
petscvp.run()