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fem_quadrilateral_solvers.py
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fem_quadrilateral_solvers.py
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# -*- coding: utf-8 -*-
"""
@author: Olav M.S. Gran
"""
from __future__ import annotations
import sys
from importlib.util import find_spec
from itertools import product, repeat
from pathlib import Path
from typing import Optional, Tuple, Callable, Union, List
from scipy.sparse.linalg import spsolve
import numpy as np
from time import perf_counter
from scipy.special import legendre
import tqdm
from . import assembly, default_constants, helpers
from .solution_function_class import SolutionFunctionValues2D
from .base_solver import BaseSolver
from .snapshot_saver import SnapshotSaver
from .matrix_least_squares import MatrixLSQ, mls_compute_from_fit
from .pod import PodWithEnergyNorm
from .error_computers import HfErrorComputer, RbErrorComputer
from .plotting import plot_mesh, plot_hf_displacment, plot_rb_displacment, plot_rb_von_mises, plot_hf_von_mises, \
plot_pod_mode
from .rb_model_saver_and_loader import RBModelSaver, RBModelLoader
from .matrix_least_square_saver_and_loader import MLSSaver, MLSLoader
from .stress_recovery import get_von_mises_stress, get_nodal_stress
symengine_is_found = (find_spec("symengine") is not None)
if symengine_is_found:
import symengine as sym
from symengine import Lambdify as sym_Lambdify
else:
import sympy as sym
from sympy import lambdify as sym_Lambdify
x1, x2 = sym.symbols("x1, x2", real=True)
sym_x_vec = sym.Matrix([x1, x2])
mu1, mu2, mu3, mu4, mu5, mu6 = sym.symbols("mu1:7", real=True)
lx, ly = sym.symbols("Lx, Ly", real=True)
x0, y0 = sym.symbols("x0, y0", real=True)
def _sym_kron_product2x2(mat1: sym.Matrix, mat2: sym.Matrix) -> sym.Matrix:
kron = sym.Matrix(
[[mat1[0, 0] * mat2[0, 0], mat1[0, 0] * mat2[0, 1], mat1[0, 1] * mat2[0, 0], mat1[0, 1] * mat2[0, 1]],
[mat1[0, 0] * mat2[1, 0], mat1[0, 0] * mat2[1, 1], mat1[0, 1] * mat2[1, 0], mat1[0, 1] * mat2[1, 1]],
[mat1[1, 0] * mat2[0, 0], mat1[1, 0] * mat2[0, 1], mat1[1, 1] * mat2[0, 0], mat1[1, 1] * mat2[0, 1]],
[mat1[1, 0] * mat2[1, 0], mat1[1, 0] * mat2[1, 1], mat1[1, 1] * mat2[1, 0], mat1[1, 1] * mat2[1, 1]]]
)
return kron
class QuadrilateralSolver(BaseSolver):
ref_plate = (0, 1)
implemented_elements = ["triangle triangle", "lt", "bilinear rectangle", "br"]
sym_phi = sym.Matrix([
x0 + x1 + mu1 * x1 * (1 - x2) + mu3 * x1 * x2 + mu5 * (1 - x1) * x2,
y0 + x2 + mu2 * x1 * (1 - x2) + mu4 * x1 * x2 + mu6 * (1 - x1) * x2
])
sym_params = sym.Matrix([x1, x2, mu1, mu2, mu3, mu4, mu5, mu6])
geo_param_range = default_constants.QS_range # (-0.1, 0.1) abs(...)< 1/10 < 1/6 = 0.1666...
_max_geo_param_range = (-1 / 6, 1 / 6)
pod: PodWithEnergyNorm
mls: MatrixLSQ
_solver_type = "QuadrilateralSolver"
_solver_type_short = "QS"
def set_geo_param_range(self, geo_range: Tuple[float, float]):
if self._max_geo_param_range[0] < geo_range[0] < geo_range[1] < self._max_geo_param_range[1]:
pass
else:
raise ValueError(f"Geometry range is larger than the valid range. Range is {geo_range}. "
f"Largest valid range is {self._max_geo_param_range}, not including the endpoints.")
self.geo_param_range = geo_range
@property
def solver_type(self) -> str:
return self._solver_type
@property
def solver_type_short(self) -> str:
return self._solver_type_short
@property
def max_geo_param_range(self) -> Tuple[float, float]:
return self._max_geo_param_range
def _check_in_geo_range(self, geo_param: float):
if self.geo_param_range[0] <= geo_param <= self.geo_param_range[1]:
pass
else:
raise ValueError(f"Geometry parameter is outside of chosen parameter range. "
f"{geo_param} not in {self.geo_param_range}.")
@staticmethod
def mu_to_vertices_dict():
mu_to_vertices_dict = {"mu1": "a2 - 1", "mu2": "b2",
"mu3": "a3 - 1", "mu4": "b3 - 1",
"mu5": "a4", "mu6": "b4 - 1"}
print("(x0, y0): are the coordinates of the lower left corner, default (0,0)")
print("Given the Quadrilateral centered in (0, 0) with vertices in (0, 0), (a2, b2), (a3, b3) and (a4, "
"b4) the parameters mu1:6 are given as:")
print(mu_to_vertices_dict)
def __init__(self, n: int, f_func: Union[Callable, int],
dirichlet_bc_func: Optional[Callable] = None, get_dirichlet_edge_func: Optional[Callable] = None,
neumann_bc_func: Optional[Callable] = None, bcs_are_on_reference_domain: bool = True,
element: str = "br", x0: float = 0, y0: float = 0):
self._uh_rom_non_recovered = None
self._geo_params = None
self._a1_set_n_rom_list = None
self._a2_set_n_rom_list = None
self._f0_set_n_rom_list = None
self._f1_dir_set_n_rom_list = None
self._f2_dir_set_n_rom_list = None
self._last_n_rom = -1
self.uh_rom = SolutionFunctionValues2D()
self.f2_dir_rom_list = None
self.f1_dir_rom_list = None
self.f0_rom_list = None
self.a2_rom_list = None
self.a1_rom_list = None
self._pod_is_computed = False
self._mls_is_computed = False
self.rb_root = None
self.hf_root = None
self.mls_root = None
self.mls_has_been_setup = False
self.uh = SolutionFunctionValues2D()
self.neumann_edge = np.array([])
self.dirichlet_edge = np.array([])
self.mls_order = 1
self.use_negative_mls_order = None
self._n = n + 1
self.n_full = self._n * self._n * 2
self.is_assembled_and_free = False
self.is_assembled_and_free_from_root = False
self.is_rb_from_root = False
self.bcs_are_on_reference_domain = bcs_are_on_reference_domain
self.lower_left_corner = (x0, y0)
self._sym_setup()
# save user inputted functions
self.input_f_func = f_func
self.input_dirichlet_bc_func = dirichlet_bc_func
self.input_get_dirichlet_edge_func = get_dirichlet_edge_func
self.input_neumann_bc_func = neumann_bc_func
if element.lower() in self.implemented_elements:
self.element = element.lower()
else:
error_text = "Element " + str(element) + " is not implemented. " \
+ "Implemented elements: " + str(self.implemented_elements)
raise NotImplementedError(error_text)
if self.element in ("triangle triangle", "lt"):
print(f"Waring: the mapping to the reference element is bilinear, linear triangle elements are "
f"therefore not ideal, try bilinear rectangle elements (default).", file=sys.stderr)
self.nq = 4
self.nq_y = None
else:
self.nq = 2
self.nq_y = 2
def default_func(x, y):
return 0, 0
# body force function
self.f_func_non_zero = True
if f_func == 0:
# f_func = 0
self.f_func = helpers.VectorizedFunction2D(default_func)
self.f_func_non_zero = False
elif isinstance(f_func, int):
raise ValueError("Only int-value for f_func allowed is 0.")
else:
if self.bcs_are_on_reference_domain:
self.f_func = helpers.VectorizedFunction2D(
lambda x, y: self.phi(*f_func(x, y), *self._geo_params))
else:
self.f_func = helpers.VectorizedFunction2D(
lambda x, y:
f_func(*self.phi(x, y, *self._geo_params)) * self.det_jac_func(x, y, *self._geo_params))
# dirichlet bc function
self.has_non_homo_dirichlet = False
if dirichlet_bc_func is None:
# dirichlet_bc_func = 0
self.dirichlet_bc_func = helpers.VectorizedFunction2D(default_func)
else:
if self.bcs_are_on_reference_domain:
self.dirichlet_bc_func = helpers.VectorizedFunction2D(
lambda x, y: self.phi(*dirichlet_bc_func(x, y), *self._geo_params))
else:
# no det_jac here implemented via a1 and a2
self.dirichlet_bc_func = helpers.VectorizedFunction2D(
lambda x, y: dirichlet_bc_func(*self.phi(x, y, *self._geo_params)))
self.has_non_homo_dirichlet = True
# get_dirichlet_edge function
if get_dirichlet_edge_func is None:
self.get_dirichlet_edge_func = None
else:
if self.bcs_are_on_reference_domain:
self.get_dirichlet_edge_func = get_dirichlet_edge_func
else:
def get_dir_edge_func(x, y):
return get_dirichlet_edge_func(*self.phi(x, y, *self._geo_params))
self.get_dirichlet_edge_func = get_dir_edge_func
# neumann bc function
self.has_non_homo_neumann = False
if self.get_dirichlet_edge_func is None:
if neumann_bc_func is not None:
error_text = "Have neumann and dirichlet conditions, " \
+ "but no function giving the neumann and dirichlet edges. "
raise ValueError(error_text)
else:
if neumann_bc_func is None:
# neumann_bc_func = 0
self.neumann_bc_func = helpers.VectorizedFunction2D(default_func)
else:
if self.bcs_are_on_reference_domain:
self.neumann_bc_func = helpers.VectorizedFunction2D(
lambda x, y: self.phi(*neumann_bc_func(x, y), *self._geo_params))
else:
self.neumann_bc_func = helpers.VectorizedFunction2D(
lambda x, y: neumann_bc_func(*self.phi(x, y, *self._geo_params)) * self.det_jac_func(
x, y, *self._geo_params))
self.has_non_homo_neumann = True
def _from_root(self):
# we choose to not update to Compressed versions
from matrix_lsq import Snapshot
root_mean = self.hf_root / "mean"
mean_snapshot = Snapshot(root_mean)
solver_type = mean_snapshot["solver_type"][0]
if not (solver_type == self.solver_type or solver_type == self.solver_type_short):
raise ValueError(f"{self.hf_root} is for {solver_type} not {self.solver_type}.")
self.geo_param_range = mean_snapshot["ranges"][0]
self.p, self.tri, self.edge = mean_snapshot["p"], mean_snapshot["tri"], mean_snapshot["edge"]
self.dirichlet_edge = mean_snapshot["dirichlet_edge"]
self.neumann_edge = mean_snapshot["neumann_edge"]
self.has_non_homo_dirichlet = (self.hf_root / "object-0" / "obj-f1_dir.npy").exists()
if self.has_non_homo_dirichlet:
self.rg = mean_snapshot["rg"]
# note here it does not matter if we have non-homogeneous or not, or if we have neumann conditions
mls_and_llc = mean_snapshot["mls_order_and_llc"]
self.mls_order = int(mls_and_llc[0])
# get lower_left_corner
self.lower_left_corner = tuple(mls_and_llc[1:])
# update phi, note do not have f_func, dirichlet_bc and neumann_bc func so 0,0 was used in cls() call.
self.sym_phi = self.sym_phi + sym.Matrix(self.lower_left_corner)
self.phi = sym_Lambdify(self.sym_params, self.sym_phi)
# compute free indexes.
self._compute_free_and_expanded_edges()
self.n_full = self.p.shape[0] * 2
self.n_free = self.expanded_free_index.shape[0]
self._n = int(np.sqrt(self.p.shape[0]))
self.is_assembled_and_free_from_root = True
# load rb
if self.rb_root is not None:
self.pod = PodWithEnergyNorm(self.hf_root)
rb_loader = RBModelLoader(self.rb_root)
rb_loader(self)
geo_gird, material_grid, num_geo_param = mean_snapshot["grid_params"]
self.pod.ns = geo_gird ** num_geo_param * material_grid ** 2
self.is_rb_from_root = True
# load mls
if self.mls_root is not None:
self.mls = MatrixLSQ(self.hf_root)
mls_loader = MLSLoader(self.mls_root)
mls_loader(self)
self._mls_is_computed = True
if self.is_rb_from_root:
self.is_rb_from_root = False
self._pod_is_computed = True
@classmethod
def from_root(cls, root: Path, rb_root: Optional[Path] = None, mls_root: Optional[Path] = None):
out = cls(2, 0)
out.hf_root = root
if rb_root is None:
# try to generate from hf_root
if (rb_root := out.gen_rb_root_from_hf_root).exists():
out.rb_root = rb_root
else:
out.rb_root = rb_root
if mls_root is None:
# try to generate from hf_root
if (mls_root := out.gen_mls_root_from_hf_root).exists():
out.mls_root = mls_root
else:
out.rb_root = mls_root
out._from_root()
return out
@property
def n(self) -> int:
return self._n - 1
def _sym_setup(self):
self.sym_phi = self.sym_phi.subs({x0: self.lower_left_corner[0], y0: self.lower_left_corner[1]})
self.sym_geo_params = self.sym_params[2:]
self.phi = sym_Lambdify(self.sym_params, self.sym_phi)
self.sym_jac = self.sym_phi.jacobian(sym_x_vec)
self.sym_det_jac = self.sym_jac.det().expand()
self.det_jac_func = sym_Lambdify(self.sym_params, self.sym_det_jac)
self.is_jac_constant = (x1 and x2 not in self.sym_jac.free_symbols)
sym_jac_inv_det = sym.Matrix([[self.sym_jac[1, 1], - self.sym_jac[0, 1]],
[-self.sym_jac[1, 0], self.sym_jac[0, 0]]])
self.jac_phi_inv = sym_Lambdify(self.sym_params, sym_jac_inv_det / self.sym_det_jac)
self.sym_z_mat = _sym_kron_product2x2(sym_jac_inv_det, sym_jac_inv_det) / self.sym_det_jac
self.z_mat_funcs = np.empty((4, 4), dtype=object)
for i in range(4):
for j in range(4):
self.z_mat_funcs[i, j] = np.vectorize(sym_Lambdify(self.sym_params, self.sym_z_mat[i, j]),
otypes=[float])
def vectorized_phi(self, x_vec: Union[int, float, List[Union[float, int]], np.ndarray],
y_vec: Union[int, float, List[Union[float, int]], np.ndarray],
*geo_params: float) -> np.ndarray:
try:
for geo_parm in geo_params:
self._check_in_geo_range(geo_parm)
except ValueError as e:
print(e, file=sys.stderr)
if isinstance(x_vec, (float, int)):
x_vec = np.array([x_vec])
if isinstance(y_vec, (float, int)):
y_vec = np.array([y_vec])
x_vals = np.zeros_like(x_vec, dtype=float)
y_vals = np.zeros_like(x_vec, dtype=float)
for i, (x, y) in enumerate(zip(x_vec, y_vec)):
x_vals[i], y_vals[i] = self.phi(x, y, *geo_params)
return np.column_stack((x_vals, y_vals))
def _sym_mls_params_setup(self):
# The construction and thereby the evaluation of the Legendre Polynomials is not optimal,
# however, rewriting this is out of scoop for the current thesis.
ant = len(self.sym_geo_params)
# get c
c_orders = np.array(list(product(*repeat(np.arange(self.mls_order + 2), ant))))
c_orders = c_orders[np.argwhere(np.sum(c_orders, axis=1) <= self.mls_order + 2).ravel()]
# get k and put it all together
mls_orders = [np.zeros(ant, dtype=int)]
# get k_term from det(jac) by setting x1=x2=0
# k_term = self.sym_det_jac.subs({x1: 0, x2: 0})
if self.solver_type == "ScalableRectangleSolver":
k_orders = [np.zeros(ant, dtype=int)]
# Jacobian is constant, i.e k is constant
# k has one component, that is PI_{i=1} mu_i
k_order = - np.ones(ant, dtype=int)
# k_order[-1] = 0 # set total to zero, we only have one term
k_orders.append(k_order)
for order1 in k_orders:
for order2 in c_orders:
sum_order = order1 + order2
mls_orders.append(sum_order)
mls_orders = np.unique(mls_orders, axis=0)
else:
# DraggableCornerRectangleSolver and QuadrilateralSolver
# nothing to do
mls_orders = c_orders
# get orders to use
arg_order = np.array(list(np.all(np.abs(order) <= self.mls_order)
and ((np.where(order > 0, order, 0).sum() <= self.mls_order)
and (-np.where(order < 0, order, 0).sum()) <= self.mls_order)
for order in mls_orders)) # back to old, add [:-1] on orders both in np.where
mls_orders = mls_orders[arg_order]
p_list = [legendre(p).coeffs[::-1] for p in range(self.mls_order + 1)]
# make the mls_funcs
sym_mls_funcs = sym.Matrix([sym.S.One] * len(mls_orders))
# shift input to polynomials to (a, b)
a_plus_b = self.geo_param_range[0] + self.geo_param_range[1]
b_minus_a_1 = 1 / (self.geo_param_range[1] - self.geo_param_range[0])
def shift(x):
return (2 * x - a_plus_b) * b_minus_a_1
for n, order in enumerate(mls_orders):
for i, mu_i in enumerate(self.sym_geo_params): # may need changing...
if order[i] >= 0:
# get legendre
p = p_list[order[i]]
poly = sym.S.Zero
for k in range(order[i] + 1):
if abs(pk := p[k]) > 1e-10:
# shift the polynomials to (a, b)
poly += pk * shift(mu_i) ** k
if poly != 0:
sym_mls_funcs[n] *= poly
else:
sym_mls_funcs[n] *= mu_i ** order[i]
# sort the terms in rising absolute order
if find_spec("symengine") is not None:
self.sym_mls_funcs = sym.Matrix(sym_mls_funcs[np.argsort(np.sum(np.abs(mls_orders), axis=1))]).T
else:
self.sym_mls_funcs = sym.Matrix(np.asarray(sym_mls_funcs)[np.argsort(np.sum(np.abs(mls_orders), axis=1))]).T
# lambdify
self.mls_funcs = sym_Lambdify(self.sym_geo_params, self.sym_mls_funcs)
def set_quadrature_scheme_order(self, nq: int, nq_y: Optional[int] = None):
if self.element in ("triangle triangle", "lt"):
self.nq = nq
else:
self.nq = nq
if nq_y is None:
self.nq_y = nq
else:
self.nq_y = nq_y
def _edges(self):
# dirichlet edge
if self.get_dirichlet_edge_func is not None:
dirichlet_edge_func_vec = np.vectorize(self.get_dirichlet_edge_func, otypes=[bool])
index = dirichlet_edge_func_vec(self.p[self.edge, 0], self.p[self.edge, 1]).all(axis=1)
if index.any():
self.dirichlet_edge = self.edge[index, :]
else:
error_text = "Only neumann conditions are not allowed, gives neumann_edge=edge, " \
+ "please define get_dirichlet_edge_func."
raise ValueError(error_text)
else:
self.dirichlet_edge = self.edge
# neumann edge
if self.dirichlet_edge.shape != self.edge.shape:
neumann_edge = np.array(list(set(map(tuple, self.edge)) - set(map(tuple, self.dirichlet_edge))))
self.neumann_edge = neumann_edge[np.argsort(neumann_edge[:, 0]), :]
else:
self.neumann_edge = np.array([])
if (self.get_dirichlet_edge_func is not None) and np.all(self.dirichlet_edge.shape == self.edge.shape):
raise ValueError("get_dirichlet_edge_func gives dirichlet_edge=edge and neumann_edge=None.")
def _compute_free_and_expanded_edges(self):
# find the unique dirichlet edge index
self.dirichlet_edge_index = np.unique(self.dirichlet_edge)
# free index is unique index minus dirichlet edge index
self.free_index = np.setdiff1d(self.tri, self.dirichlet_edge_index)
self.expanded_free_index = helpers.expand_index(self.free_index)
self.expanded_dirichlet_edge_index = helpers.expand_index(self.dirichlet_edge_index)
def _set_free(self):
free_xy_index = np.ix_(self.expanded_free_index, self.expanded_free_index)
self.a1 = self.a1_full[free_xy_index]
self.a2 = self.a2_full[free_xy_index]
self.f0 = self.f0_full[self.expanded_free_index]
def _set_f_load_dirichlet(self):
# compute a_dirichlet
# x and y on the dirichlet_edge
x_vec = self.p[self.dirichlet_edge_index][:, 0]
y_vec = self.p[self.dirichlet_edge_index][:, 1]
# lifting function
self.rg = helpers.FunctionValues2D.from_2xn(self.dirichlet_bc_func(x_vec, y_vec)).flatt_values
dirichlet_xy_index = np.ix_(self.expanded_free_index, self.expanded_dirichlet_edge_index)
self.f1_dir = self.a1_full[dirichlet_xy_index] @ self.rg
self.f2_dir = self.a2_full[dirichlet_xy_index] @ self.rg
def _assemble(self, geo_params):
for geo_parm in geo_params:
self._check_in_geo_range(geo_parm)
self._geo_params = geo_params
if self.element in ("triangle triangle", "lt"):
self.p, self.tri, self.edge = assembly.triangle.get_plate.getPlate(self._n)
self.a1_full, self.a2_full, self.f0_full \
= assembly.triangle.linear.assemble_a1_a2_and_f_body_force(self._n, self.p, self.tri,
self.z_mat_funcs, self._geo_params,
self.f_func, self.f_func_non_zero,
self.nq)
if self.has_non_homo_neumann:
self.f0_full += assembly.triangle.linear.assemble_f_neumann(self._n, self.p, self.neumann_edge,
self.neumann_bc_func, self.nq)
else:
self.p, self.tri, self.edge = assembly.rectangle.get_plate.getPlate(self._n)
self.a1_full, self.a2_full, self.f0_full \
= assembly.rectangle.bilinear.assemble_a1_a2_and_f_body_force(self._n, self.p, self.tri,
self.z_mat_funcs, self._geo_params,
self.f_func, self.f_func_non_zero,
self.nq, self.nq_y)
if self.has_non_homo_neumann:
self.f0_full += assembly.rectangle.bilinear.assemble_f_neumann(self._n, self.p, self.neumann_edge,
self.neumann_bc_func,
self.nq * self.nq_y)
self.a1_full = self.a1_full.tocsr()
self.a2_full = self.a2_full.tocsr()
self._edges()
self._compute_free_and_expanded_edges()
self.n_free = self.expanded_free_index.shape[0]
self._set_free()
if self.has_non_homo_dirichlet:
self._set_f_load_dirichlet()
self.is_assembled_and_free = True
def assemble(self, mu1: float, mu2: float, mu3: float, mu4: float, mu5: float, mu6: float):
self._assemble(np.array([mu1, mu2, mu3, mu4, mu5, mu6]))
def hfsolve(self, e_young: float, nu_poisson: float, *geo_params: Optional[float], print_info: bool = True):
start_time = perf_counter()
if len(geo_params) != 0:
if len(geo_params) != len(self.sym_geo_params):
raise ValueError(
f"To many geometry parameters, got {len(geo_params)} expected {len(self.sym_geo_params)}.")
for geo_param in geo_params:
self._check_in_geo_range(geo_param)
self._geo_params = geo_params
if not self.mls_has_been_setup:
raise ValueError("Matrix LSQ data functions have not been setup, please call matrix_lsq_setup.")
if not self._mls_is_computed:
raise ValueError("Matrices and vectors are not computed, by Matrix LSQ.")
data = self.mls_funcs(*geo_params)
a1_fit = mls_compute_from_fit(data, self.mls.a1_list)
a2_fit = mls_compute_from_fit(data, self.mls.a2_list)
f_load = mls_compute_from_fit(data, self.mls.f0_list)
a = helpers.compute_a(e_young, nu_poisson, a1_fit, a2_fit)
if self.has_non_homo_dirichlet:
f1_dir_fit = mls_compute_from_fit(data, self.mls.f1_dir_list)
f2_dir_fit = mls_compute_from_fit(data, self.mls.f2_dir_list)
f_load -= helpers.compute_a(e_young, nu_poisson, f1_dir_fit, f2_dir_fit)
elif self.is_assembled_and_free:
# compute a
a = helpers.compute_a(e_young, nu_poisson, self.a1, self.a2)
# copy the body force load vector
f_load = self.f0.copy()
# compute and add the dirichlet load vector if it exists
if self.has_non_homo_dirichlet:
f_load -= helpers.compute_a(e_young, nu_poisson, self.f1_dir, self.f2_dir)
elif self.is_assembled_and_free_from_root:
raise ValueError("Matrices and vectors are assembled from saved data, geo_params must therefor be given.")
else:
raise ValueError("Matrices and vectors are not assembled.")
# initialize uh
uh = np.zeros(self.n_full)
# solve system
uh[self.expanded_free_index] = spsolve(a, f_load)
if self.has_non_homo_dirichlet:
uh[self.expanded_dirichlet_edge_index] = self.rg
if print_info:
print("Solved a @ uh = f_load in {:.6f} sec".format(perf_counter() - start_time))
# set uh, and save it in a nice way.
self.uh = SolutionFunctionValues2D.from_1x2n(uh)
self.uh.set_geo_params(self._geo_params)
self.uh.set_e_young_and_nu_poisson(e_young, nu_poisson)
if print_info:
print("Get solution by the property uh, uh_free or uh_full of the class.\n" +
"The property uh, extra properties values, x and y are available.\n")
def rbsolve_uh_rom_non_recovered(self, e_young: float, nu_poisson: float, *geo_params: float,
n_rom: Optional[int] = None, print_info: bool = True):
start_time = perf_counter()
if len(geo_params) != len(self.sym_geo_params):
raise ValueError(
f"To many geometry parameters, got {len(geo_params)} expected {len(self.sym_geo_params)}.")
for geo_param in geo_params:
self._check_in_geo_range(geo_param)
self._geo_params = geo_params
if not self.mls_has_been_setup:
raise ValueError("Matrix LSQ data functions have not been setup, please call matrix_lsq_setup.")
if self.is_rb_from_root:
if n_rom is None:
data = self.mls_funcs(*geo_params)
a1_fit_rom = mls_compute_from_fit(data, self.a1_rom_list)
a2_fit_rom = mls_compute_from_fit(data, self.a2_rom_list)
f_load_rom = mls_compute_from_fit(data, self.f0_rom_list)
a_rom = helpers.compute_a(e_young, nu_poisson, a1_fit_rom, a2_fit_rom)
if self.has_non_homo_dirichlet:
f1_dir_fit_rom = mls_compute_from_fit(data, self.f1_dir_rom_list)
f2_dir_fit_rom = mls_compute_from_fit(data, self.f2_dir_rom_list)
f_load_rom -= helpers.compute_a(e_young, nu_poisson, f1_dir_fit_rom, f2_dir_fit_rom)
else:
raise ValueError("Can not set n_rom when loading RB model from root without "
"calling matrix_least_squares first.")
else:
if not self._mls_is_computed:
raise ValueError("Matrices and vectors are not computed, by Matrix LSQ.")
if not self._pod_is_computed:
raise ValueError("Pod is not computed. Can not solve.")
if (n_rom is None) or (self.pod.n_rom == n_rom):
data = self.mls_funcs(*geo_params)
a1_fit_rom = mls_compute_from_fit(data, self.a1_rom_list)
a2_fit_rom = mls_compute_from_fit(data, self.a2_rom_list)
f_load_rom = mls_compute_from_fit(data, self.f0_rom_list)
a_rom = helpers.compute_a(e_young, nu_poisson, a1_fit_rom, a2_fit_rom)
if self.has_non_homo_dirichlet:
f1_dir_fit_rom = mls_compute_from_fit(data, self.f1_dir_rom_list)
f2_dir_fit_rom = mls_compute_from_fit(data, self.f2_dir_rom_list)
f_load_rom -= helpers.compute_a(e_young, nu_poisson, f1_dir_fit_rom, f2_dir_fit_rom)
else:
if (self._last_n_rom != n_rom) or (self._a1_set_n_rom_list is None):
self._a1_set_n_rom_list = [self.pod.compute_rom(obj, n_rom=n_rom) for obj in self.mls.a1_list]
self._a2_set_n_rom_list = [self.pod.compute_rom(obj, n_rom=n_rom) for obj in self.mls.a2_list]
self._f0_set_n_rom_list = [self.pod.compute_rom(obj, n_rom=n_rom) for obj in self.mls.f0_list]
data = self.mls_funcs(*geo_params)
a1_fit_rom = mls_compute_from_fit(data, self._a1_set_n_rom_list)
a2_fit_rom = mls_compute_from_fit(data, self._a2_set_n_rom_list)
f_load_rom = mls_compute_from_fit(data, self._f0_set_n_rom_list)
a_rom = helpers.compute_a(e_young, nu_poisson, a1_fit_rom, a2_fit_rom)
if self.has_non_homo_dirichlet:
if (self._last_n_rom != n_rom) or (self._f1_dir_set_n_rom_list is None):
self._f1_dir_set_n_rom_list = [self.pod.compute_rom(obj, n_rom=n_rom)
for obj in self.mls.f1_dir_list]
self._f2_dir_set_n_rom_list = [self.pod.compute_rom(obj, n_rom=n_rom)
for obj in self.mls.f2_dir_list]
f1_dir_fit_rom = mls_compute_from_fit(data, self._f1_dir_set_n_rom_list)
f2_dir_fit_rom = mls_compute_from_fit(data, self._f2_dir_set_n_rom_list)
f_load_rom -= helpers.compute_a(e_young, nu_poisson, f1_dir_fit_rom, f2_dir_fit_rom)
# set last n_rom
self._last_n_rom = n_rom
# solve and project rb solution
self._uh_rom_non_recovered = np.linalg.solve(a_rom, f_load_rom)
if print_info:
print("Solved a_rom @ uh_rom = f_load_rom in {:.6f} sec".format(perf_counter() - start_time))
def rbsolve_uh_rom_recovered(self, e_young: float, nu_poisson: float, *geo_params: float,
n_rom: Optional[int] = None, print_info: bool = True):
self.rbsolve_uh_rom_non_recovered(e_young, nu_poisson, *geo_params, n_rom=n_rom, print_info=print_info)
# initialize uh
uh_rom = np.zeros(self.n_full)
# project rb solution
if n_rom is None:
uh_rom[self.expanded_free_index] = self.pod.v @ self._uh_rom_non_recovered
else:
uh_rom[self.expanded_free_index] = self.pod.get_v_mat(n_rom) @ self._uh_rom_non_recovered
if self.has_non_homo_dirichlet:
# lifting function
uh_rom[self.expanded_dirichlet_edge_index] = self.rg
# set uh_rom, save it in a nice way.
self.uh_rom = SolutionFunctionValues2D.from_1x2n(uh_rom)
self.uh_rom.set_geo_params(self._geo_params)
self.uh_rom.set_e_young_and_nu_poisson(e_young, nu_poisson)
if print_info:
print("Get solution by the property uh_rom, uh_rom_free or uh_rom_full of the class.\n" +
"The property uh_rom, extra properties values, x and y are available.\n")
def rbsolve(self, e_young: float, nu_poisson: float, *geo_params: float, n_rom: Optional[int] = None,
print_info: bool = True):
# short for rbsolve_uh_rom_recovered
self.rbsolve_uh_rom_recovered(e_young, nu_poisson, *geo_params, n_rom=n_rom, print_info=print_info)
def hferror(self, e_young: float, nu_poisson: float, *geo_params: Optional[float],
root: Optional[Path] = None) -> float:
if root is not None:
if self.hf_root is not None:
if self.hf_root != root:
print(f"Warning: root and saved hf_root do not match. <{root}> v. <{self.hf_root}>.",
file=sys.stderr)
self.hf_root = root
else:
if self.hf_root is None:
raise ValueError("hf_root is None, root must be given.")
# get relative HF error between true HF and MatrixLSQ HF systems
hf_err_comp = HfErrorComputer(self.hf_root)
return hf_err_comp(self, e_young, nu_poisson, *geo_params)
def rberror(self, e_young: float, nu_poisson: float, *geo_params: float,
n_rom: Optional[int] = None, root: Optional[Path] = None) -> float:
if root is not None:
if self.hf_root is not None:
if self.hf_root != root:
print(f"Warning: root and saved hf_root do not match. <{root}> v. <{self.hf_root}>.",
file=sys.stderr)
self.hf_root = root
else:
if self.hf_root is None:
raise ValueError("hf_root is None, root must be given.")
# get relative RB error between true HF and RB systems
rb_err_comp = RbErrorComputer(self.hf_root)
return rb_err_comp(self, e_young, nu_poisson, *geo_params, n_rom=n_rom)
def hf_nodal_stress(self, print_info=True):
if self.uh.values is None:
raise ValueError("High fidelity Problem has not been solved.")
get_nodal_stress(self, compute_for_rb=False)
if print_info:
print("Get nodal stress by the property uh.nodal_stress of the class.")
def rb_nodal_stress(self, print_info=True):
if self.uh_rom.values is None:
raise ValueError("Reduced order Problem has not been solved.")
get_nodal_stress(self, compute_for_rb=True)
if print_info:
print("Get nodal stress by the property uh_rom.nodal_stress of the class.")
def hf_von_mises_stress(self, print_info=True):
if self.uh.values is None:
raise ValueError("High fidelity Problem has not been solved.")
if self.uh.nodal_stress is None:
self.hf_nodal_stress(print_info=False)
get_von_mises_stress(self, compute_for_rb=False)
if print_info:
print("Get von Mises yield by the property uh.von_mises of the class.")
def rb_von_mises_stress(self, print_info=True):
if self.uh_rom.values is None:
raise ValueError("Reduced order Problem has not been solved.")
if self.uh_rom.nodal_stress is None:
self.rb_nodal_stress(print_info=False)
get_von_mises_stress(self, compute_for_rb=True)
if print_info:
print("Get von Mises yield by the property uh_rom.von_mises of the class.")
def save_snapshots(self, root: Path, geo_grid: int,
mode: str = "uniform",
material_grid: Optional[int] = None,
e_young_range: Optional[Tuple[float, float]] = None,
nu_poisson_range: Optional[Tuple[float, float]] = None):
self.hf_root = root
if not self.mls_has_been_setup:
raise ValueError("Matrix LSQ data functions have not been setup, please call matrix_lsq_setup.")
saver = SnapshotSaver(self.hf_root, geo_grid, self.geo_param_range,
mode=mode,
material_grid=material_grid,
e_young_range=e_young_range,
nu_poisson_range=nu_poisson_range)
saver(self)
def multiprocessing_save_snapshots(self, root: Path, geo_grid: int,
power_divider: int = 3,
mode: str = "uniform",
material_grid: Optional[int] = None,
e_young_range: Optional[Tuple[float, float]] = None,
nu_poisson_range: Optional[Tuple[float, float]] = None):
self.hf_root = root
if not self.mls_has_been_setup:
raise ValueError("Matrix LSQ data functions have not been setup, please call matrix_lsq_setup.")
from .multiprocessing_snapshot_saver import MultiprocessingSnapshotSaver
saver = MultiprocessingSnapshotSaver(self.hf_root, geo_grid, self.geo_param_range,
mode=mode,
material_grid=material_grid,
e_young_range=e_young_range,
nu_poisson_range=nu_poisson_range)
saver(self, power_divider=power_divider)
import sys
print(f"warning: Environmental variables have been set. This may effect further use of the solver.",
file=sys.stderr)
def matrix_lsq_setup(self, mls_order: Optional[int] = 1):
# default mls_order is 1,
assert self.mls_order >= 0
if self.mls_order != mls_order:
if mls_order != 1:
assert mls_order >= 0
self.mls_order = mls_order
# else just use set self.mls_order
self._sym_mls_params_setup()
self.mls_has_been_setup = True
def matrix_lsq(self, root: Optional[Path] = None):
if root is not None:
if self.hf_root is not None:
if self.hf_root != root:
print(f"Warning: root and saved hf_root do not match. <{root}> v. <{self.hf_root}>.",
file=sys.stderr)
self.hf_root = root
else:
if self.hf_root is None:
raise ValueError("hf_root is None, root must be given.")
if not self.mls_has_been_setup:
raise ValueError("Matrix LSQ data functions have not been setup, please call matrix_lsq_setup.")
self.mls = MatrixLSQ(self.hf_root)
self.mls()
self._mls_is_computed = True
if self.is_rb_from_root:
self.is_rb_from_root = False
self._pod_is_computed = True
def save_matrix_lsq(self, root: Optional[Path] = None):
if root is None:
self.mls_root = self.gen_mls_root_from_hf_root
else:
self.mls_root = root
if self.mls_root == self.hf_root:
raise ValueError(f"root can not be equal to hf_root: {self.hf_root}.")
if not self._mls_is_computed:
raise ValueError("Matrix LSQ is not computed.")
mls_saver = MLSSaver(self.mls_root)
mls_saver(self)
def build_rb_model(self, root: Optional[Path] = None, eps_pod: Optional[float] = None):
if root is not None:
if self.hf_root is not None:
if self.hf_root != root:
print(f"Warning: root and saved hf_root do not match. <{root}> v. <{self.hf_root}>.",
file=sys.stderr)
self.hf_root = root
else:
if self.hf_root is None:
raise ValueError("hf_root is None, root must be given.")
if not self.mls_has_been_setup:
raise ValueError("Matrix LSQ data functions have not been setup, please call matrix_lsq_setup.")
self.pod = PodWithEnergyNorm(self.hf_root, eps_pod=eps_pod)
self.pod()
self._pod_is_computed = True
if not self._mls_is_computed:
# compute matrix_lsq from root
self.matrix_lsq(root)
self.a1_rom_list = [self.pod.compute_rom(obj) for obj in self.mls.a1_list]
self.a2_rom_list = [self.pod.compute_rom(obj) for obj in self.mls.a2_list]
self.f0_rom_list = [self.pod.compute_rom(obj) for obj in self.mls.f0_list]
if self.has_non_homo_dirichlet:
self.f1_dir_rom_list = [self.pod.compute_rom(obj) for obj in self.mls.f1_dir_list]
self.f2_dir_rom_list = [self.pod.compute_rom(obj) for obj in self.mls.f2_dir_list]
self.is_rb_from_root = False
def save_rb_model(self, root: Optional[Path] = None):
if root is None:
self.rb_root = self.gen_rb_root_from_hf_root
else:
self.rb_root = root
if self.rb_root == self.hf_root:
raise ValueError(f"root can not be equal to hf_root: {self.hf_root}.")
if not self._pod_is_computed:
raise ValueError("Pod is not computed.")
rb_saver = RBModelSaver(self.rb_root)
rb_saver(self)
def plot_pod_singular_values(self):
if not self._pod_is_computed:
raise ValueError("Pod is not computed.")
self.pod.plot_singular_values()
def plot_pod_relative_information_content(self):
if not self._pod_is_computed:
raise ValueError("Pod is not computed.")
self.pod.plot_relative_information_content()
def plot_mesh(self, *geo_params: Optional[float]):
if not self.is_assembled_and_free:
if self.element in ("triangle triangle", "lt"):
self.p, self.tri, self.edge = assembly.triangle.get_plate.getPlate(self._n)
else:
self.p, self.tri, self.edge = assembly.rectangle.get_plate.getPlate(self._n)
if len(geo_params) == 0:
if self._geo_params is None:
raise ValueError("No saved geo_params, geo_params must be given.")
plot_mesh(self, *self._geo_params)
else:
plot_mesh(self, *geo_params)
def hf_plot_displacement(self):
if self.uh.values is None:
raise ValueError("High fidelity Problem has not been solved.")
plot_hf_displacment(self)
def rb_plot_displacement(self):
if self.uh_rom.values is None:
raise ValueError("Reduced Order Problem has not been solved.")
plot_rb_displacment(self)
def hf_plot_von_mises(self, levels: Optional[np.ndarray] = None):
if self.uh.von_mises is None:
self.hf_von_mises_stress(print_info=False)
plot_hf_von_mises(self, levels=levels)
def rb_plot_von_mises(self, levels: Optional[np.ndarray] = None):
if self.uh_rom.von_mises is None:
self.rb_von_mises_stress(print_info=False)
plot_rb_von_mises(self, levels=levels)
def rb_pod_mode(self, i: int) -> SolutionFunctionValues2D:
assert i >= 1
pod_mode = np.zeros(self.n_full)
# get mode form V matrix
if not (self._pod_is_computed or self.is_rb_from_root):
raise ValueError("POD is not computed or no reduced order model from root.")
pod_mode[self.expanded_free_index] = self.pod.v_mat_n_max[:, i - 1]
# lifting function
if self.has_non_homo_dirichlet:
pod_mode[self.expanded_dirichlet_edge_index] = self.rg
pod_mode = SolutionFunctionValues2D.from_1x2n(pod_mode)
pod_mode.set_geo_params(tuple([float(np.mean(self.geo_param_range)), float(np.mean(self.geo_param_range))]))
return pod_mode
def rb_plot_pod_mode(self, i: int):
plot_pod_mode(self, i)
def get_u_exact(self, u_exact_func):
if self.bcs_are_on_reference_domain:
# return helpers.get_u_exact(self.p, u_exact_func)
# print(u_exact_func(0.5, 0.5))
# print(self.phi(*u_exact_func(0.5, 0.5), *self._geo_params).ravel())
return helpers.get_u_exact(self.p, lambda x, y: self.phi(*u_exact_func(x, y), *self._geo_params).ravel())
else:
return helpers.get_u_exact(self.p, lambda x, y: u_exact_func(*self.phi(x, y, *self._geo_params)))
def get_geo_param_limit_estimate(self, num, round_decimal=6):
# 1 / det(jac) has gives a rational of form 1/(k + c*x)
# Which has the Taylor expansion
# 1 / (k + c*x) = 1/k - cx/k^2 + c^2x^2/k^3 - ... + ...
# for |x|<|k/c|
# now max|x| = 1, so we need |c| < |k|
# get k from det(jac) by setting x1=x2=0
k = self.sym_det_jac.subs({x1: 0, x2: 0})
k_func = sym_Lambdify(self.sym_geo_params, k)
# get c from det(jac) via coeff and assuming x1=x2=1
c = self.sym_det_jac.coeff(x1) + self.sym_det_jac.coeff(x2)
cx = self.sym_det_jac - k
c_func = sym_Lambdify(self.sym_geo_params, c)
cx_func = sym_Lambdify(self.sym_params, cx)
check_vec = np.linspace(0, 2 / len(self.sym_geo_params), num)
max_geo_params = 0.0
ant = len(self.sym_geo_params)
for geo_params in tqdm.tqdm(product(*repeat(check_vec, ant)), desc="Iterating"):
if abs(c_func(*geo_params)) < abs(k_func(*geo_params)):
pot_max = max(geo_params)
if (abs(c_func(*repeat(pot_max, ant))) < abs(k_func(*repeat(pot_max, ant)))) or \
(abs(c_func(*repeat(-pot_max, ant))) < abs(k_func(*repeat(-pot_max, ant)))):
if pot_max > max_geo_params:
x_vec = np.linspace(-1, 1, 101)
update_max = True
for x, y in product(x_vec, x_vec):
if not abs(cx_func(x, y, *repeat(pot_max, ant))) < abs(k_func(*repeat(pot_max, ant))):
update_max = False
break
if not abs(cx_func(x, y, *repeat(-pot_max, ant))) < abs(k_func(*repeat(-pot_max, ant))):
update_max = False
break
if update_max:
max_geo_params = pot_max
max_geo_params = round(max_geo_params, round_decimal)
print(f"The estimate limit for the parameters is ({-max_geo_params}, {max_geo_params}).")
@property
def mls_num_kept(self) -> int:
if not self._mls_is_computed:
raise ValueError("Matrix least square is not computed.")
return self.mls.num_kept
@property
def n_rom(self) -> int:
if not (self._pod_is_computed or self.is_rb_from_root):
raise ValueError("POD is not computed or no reduced order model from root.")
return self.pod.n_rom
@property
def ns_rom(self) -> int:
if not (self._pod_is_computed or self.is_rb_from_root):
raise ValueError("POD is not computed or no reduced order model from root.")
return self.pod.ns
@property
def n_rom_max(self) -> int:
if not (self._pod_is_computed or self.is_rb_from_root):
raise ValueError("POD is not computed or no reduced order model from root.")
return self.pod.n_rom_max
@property
def uh_free(self) -> np.ndarray:
if self.uh.values is None:
raise ValueError(
"High fidelity Problem has not been solved, can not return uh_free.")
return self.uh.flatt_values[self.expanded_free_index]
@property
def uh_full(self) -> np.ndarray:
if self.uh.values is None:
raise ValueError(
"High fidelity Problem has not been solved, can not return uh_full.")
return self.uh.flatt_values
@property
def uh_anorm2(self) -> np.ndarray:
if self.uh.values is None:
raise ValueError(
"High fidelity Problem has not been solved, can not return uh_anorm2.")
return self.uh.flatt_values.T @ helpers.compute_a(self.uh.e_young, self.uh.nu_poisson, self.a1_full,
self.a2_full) @ self.uh.flatt_values
@property
def uh_rom_free(self) -> np.ndarray:
if self.uh_rom.values is None:
raise ValueError(
"Reduced Order Problem has not been solved, can not return uh_free.")