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# Copyright (C) 2024-2025 Jørgen S. Dokken
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Unit tests for high-level wrapper around PETSc for linear and non-linear problems"""
from mpi4py import MPI
import numpy as np
import pytest
import basix.ufl
import dolfinx
import ufl
@pytest.mark.petsc4py
class TestPETScSolverWrappers:
@pytest.mark.parametrize(
"mode",
[dolfinx.mesh.GhostMode.none, dolfinx.mesh.GhostMode.shared_facet],
)
@pytest.mark.filterwarnings("ignore::DeprecationWarning")
def test_compare_solution_linear_vs_nonlinear_problem(self, mode):
"""Test that the wrapper for Linear problem and NonlinearProblem give the same result"""
from petsc4py import PETSc
import dolfinx.fem.petsc
import dolfinx.nls.petsc
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 12, 12, ghost_mode=mode)
V = dolfinx.fem.functionspace(msh, ("Lagrange", 1))
uh = dolfinx.fem.Function(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(msh)
f = x[0] * ufl.sin(x[1])
F = ufl.inner(uh, v) * ufl.dx - ufl.inner(f, v) * ufl.dx
u = ufl.TrialFunction(V)
a = ufl.replace(F, {uh: u})
sys = PETSc.Sys()
if MPI.COMM_WORLD.size == 1:
factor_type = "petsc"
elif sys.hasExternalPackage("mumps"):
factor_type = "mumps"
elif sys.hasExternalPackage("superlu_dist"):
factor_type = "superlu_dist"
else:
pytest.skip("No external solvers available in parallel")
petsc_options_linear = {
"ksp_type": "preonly",
"pc_type": "lu",
"pc_factor_mat_solver_type": factor_type,
}
petsc_options_prefix_linear = (
f"test_compare_solution_linear_vs_nonlinear_problem__{mode}_linear_"
)
linear_problem = dolfinx.fem.petsc.LinearProblem(
ufl.lhs(a),
ufl.rhs(a),
petsc_options_prefix=petsc_options_prefix_linear,
petsc_options=petsc_options_linear,
)
u_lin = linear_problem.solve()
assert linear_problem.solver.getConvergedReason() > 0
# Compare LinearProblem solution against the one obtained by
# legacy NewtonSolverNonlinearProblem
u_nonlin_legacy = dolfinx.fem.Function(V)
nonlinear_problem_legacy = dolfinx.fem.petsc.NewtonSolverNonlinearProblem(
ufl.replace(F, {uh: u_nonlin_legacy}), u_nonlin_legacy
)
nonlinear_solver_legacy = dolfinx.nls.petsc.NewtonSolver(msh.comm, nonlinear_problem_legacy)
ksp = nonlinear_solver_legacy.krylov_solver
ksp.setType("preonly")
ksp.getPC().setType("lu")
ksp.getPC().setFactorSolverType(factor_type)
eps = 100 * np.finfo(dolfinx.default_scalar_type).eps
nonlinear_solver_legacy.atol = eps
nonlinear_solver_legacy.rtol = eps
nonlinear_solver_legacy.solve(u_nonlin_legacy)
assert np.allclose(u_lin.x.array, u_nonlin_legacy.x.array, atol=eps, rtol=eps)
with (
u_lin.x.petsc_vec.localForm() as _u_lin,
u_nonlin_legacy.x.petsc_vec.localForm() as _u_nonlin,
):
assert np.allclose(_u_lin.array_r, _u_nonlin.array_r, atol=eps, rtol=eps)
# Compare LinearProblem solution against the one obtained by NonlinearProblem
petsc_options_nonlinear = {
"ksp_type": "preonly",
"pc_type": "lu",
"pc_factor_mat_solver_type": factor_type,
"snes_atol": eps,
"snes_rtol": eps,
}
petsc_options_prefix_nonlinear = (
f"test_compare_solution_linear_vs_nonlinear_problem__{mode}__nonlinear_"
)
u_nonlin = dolfinx.fem.Function(V)
nonlinear_problem = dolfinx.fem.petsc.NonlinearProblem(
ufl.replace(F, {uh: u_nonlin}),
u_nonlin,
petsc_options_prefix=petsc_options_prefix_nonlinear,
petsc_options=petsc_options_nonlinear,
)
nonlinear_problem.solve()
assert nonlinear_problem.solver.getConvergedReason() > 0
assert np.allclose(u_lin.x.array, u_nonlin.x.array, atol=eps, rtol=eps)
with u_lin.x.petsc_vec.localForm() as _u_lin, u_nonlin.x.petsc_vec.localForm() as _u_nonlin:
assert np.allclose(_u_lin.array_r, _u_nonlin.array_r, atol=eps, rtol=eps)
@pytest.mark.parametrize(
"mode", [dolfinx.mesh.GhostMode.none, dolfinx.mesh.GhostMode.shared_facet]
)
@pytest.mark.parametrize("kind", [None, "mpi", "nest", [["aij", None], [None, "baij"]]])
def test_mixed_system(self, mode, kind):
from petsc4py import PETSc
import dolfinx.fem.petsc
sys = PETSc.Sys()
if ((kind=="nest" or isinstance(kind, list))
and not sys.hasExternalPackage("mumps")):
pytest.skip("matrix type nest requires MUMPS")
if sys.hasExternalPackage("mumps"):
factor_type = "mumps"
elif sys.hasExternalPackage("superlu_dist"):
factor_type = "superlu_dist"
elif MPI.COMM_WORLD.size == 1:
factor_type = "petsc"
else:
pytest.skip("No external solvers available in parallel")
msh = dolfinx.mesh.create_unit_square(
MPI.COMM_WORLD, 12, 12, ghost_mode=mode, dtype=PETSc.RealType
)
def top_bc(x):
return np.isclose(x[1], 1.0)
msh.topology.create_connectivity(msh.topology.dim - 1, msh.topology.dim)
bndry_facets = dolfinx.mesh.locate_entities_boundary(msh, msh.topology.dim - 1, top_bc)
el_0 = basix.ufl.element("Lagrange", msh.basix_cell(), 1, dtype=PETSc.RealType)
el_1 = basix.ufl.element("Lagrange", msh.basix_cell(), 2, dtype=PETSc.RealType)
if kind is None:
me = basix.ufl.mixed_element([el_0, el_1])
W = dolfinx.fem.functionspace(msh, me)
V, _ = W.sub(0).collapse()
Q, _ = W.sub(1).collapse()
else:
V = dolfinx.fem.functionspace(msh, el_0)
Q = dolfinx.fem.functionspace(msh, el_1)
W = ufl.MixedFunctionSpace(V, Q)
u, p = ufl.TrialFunctions(W)
v, q = ufl.TestFunctions(W)
a00 = ufl.inner(u, v) * ufl.dx
a11 = ufl.inner(p, q) * ufl.dx
x = ufl.SpatialCoordinate(msh)
f = x[0] + 3 * x[1]
g = -(x[1] ** 2) + x[0]
L0 = ufl.inner(f, v) * ufl.dx
L1 = ufl.inner(g, q) * ufl.dx
f_expr = dolfinx.fem.Expression(f, V.element.interpolation_points)
g_expr = dolfinx.fem.Expression(g, Q.element.interpolation_points)
u_bc = dolfinx.fem.Function(V)
u_bc.interpolate(f_expr)
p_bc = dolfinx.fem.Function(Q)
p_bc.interpolate(g_expr)
if kind is None:
a = a00 + a11
L = L0 + L1
dofs_V = dolfinx.fem.locate_dofs_topological(
(W.sub(0), V), msh.topology.dim - 1, bndry_facets
)
dofs_Q = dolfinx.fem.locate_dofs_topological(
(W.sub(1), Q), msh.topology.dim - 1, bndry_facets
)
bcs = [
dolfinx.fem.dirichletbc(u_bc, dofs_V, W.sub(0)),
dolfinx.fem.dirichletbc(p_bc, dofs_Q, W.sub(1)),
]
else:
a = [[a00, None], [None, a11]]
L = [L0, L1]
dofs_V = dolfinx.fem.locate_dofs_topological(V, msh.topology.dim - 1, bndry_facets)
dofs_Q = dolfinx.fem.locate_dofs_topological(Q, msh.topology.dim - 1, bndry_facets)
bcs = [
dolfinx.fem.dirichletbc(u_bc, dofs_V),
dolfinx.fem.dirichletbc(p_bc, dofs_Q),
]
petsc_options_prefix = (
f"test_mixed_system_{kind if isinstance(kind, str) else 'nest_2d_list'}_"
)
petsc_options = {
"ksp_type": "preonly",
"pc_type": "lu",
"pc_factor_mat_solver_type": factor_type,
"ksp_error_if_not_converged": True,
}
problem = dolfinx.fem.petsc.LinearProblem(
a,
L,
bcs=bcs,
kind=kind,
petsc_options_prefix=petsc_options_prefix,
petsc_options=petsc_options,
)
wh = problem.solve()
assert problem.solver.getConvergedReason() > 0
if kind is None:
uh, ph = wh.split()
else:
uh, ph = wh
error_uh = dolfinx.fem.form(ufl.inner(uh - f, uh - f) * ufl.dx)
error_ph = dolfinx.fem.form(ufl.inner(ph - g, ph - g) * ufl.dx)
local_uh_L2 = dolfinx.fem.assemble_scalar(error_uh)
local_ph_L2 = dolfinx.fem.assemble_scalar(error_ph)
global_uh_L2 = np.sqrt(msh.comm.allreduce(local_uh_L2, op=MPI.SUM))
global_ph_L2 = np.sqrt(msh.comm.allreduce(local_ph_L2, op=MPI.SUM))
tol = 500 * np.finfo(dolfinx.default_scalar_type).eps
assert global_uh_L2 < tol and global_ph_L2 < tol
|
