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# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier: MIT
from __future__ import annotations
from mpi4py import MPI
from petsc4py import PETSc
import numpy as np
import numpy.testing as nt
import pytest
import scipy.sparse.linalg
import ufl
from dolfinx import default_scalar_type, fem
from dolfinx.common import Timer, TimingType, list_timings
from dolfinx.mesh import create_unit_square
import dolfinx_mpc
import dolfinx_mpc.utils
from dolfinx_mpc.utils import get_assemblers # noqa: F401
@pytest.mark.parametrize("get_assemblers", ["C++"], indirect=True)
@pytest.mark.parametrize("master_point", [[1, 1], [0, 1]])
def test_pipeline(master_point, get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 3, 5)
V = fem.functionspace(mesh, ("Lagrange", 1))
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
d = fem.Constant(mesh, default_scalar_type(1.5))
c = fem.Constant(mesh, default_scalar_type(2))
x = ufl.SpatialCoordinate(mesh)
f = c * ufl.sin(2 * ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
g = fem.Function(V)
g.interpolate(lambda x: np.sin(x[0]) * x[1])
h = fem.Function(V)
h.interpolate(lambda x: 2 + x[1] * x[0])
a = d * g * ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
rhs = h * ufl.inner(f, v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
# Create multipoint constraint
def l2b(li):
return np.array(li, dtype=mesh.geometry.x.dtype).tobytes()
s_m_c = {
l2b([1, 0]): {l2b([0, 1]): 0.43, l2b([1, 1]): 0.11},
l2b([0, 0]): {l2b(master_point): 0.69},
}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
A = assemble_matrix(bilinear_form, mpc)
b = assemble_vector(linear_form, mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
solver = PETSc.KSP().create(mesh.comm)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
solver.setOperators(A)
# Solve
uh = fem.Function(mpc.function_space)
uh.x.array[:] = 0
solver.solve(b, uh.x.petsc_vec)
uh.x.scatter_forward()
mpc.backsubstitution(uh)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
is_complex = np.issubdtype(default_scalar_type, np.complexfloating) # type: ignore
scipy_dtype = np.complex128 if is_complex else np.float64
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh.x.petsc_vec, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T.astype(scipy_dtype) * A_csr.astype(scipy_dtype) * K.astype(scipy_dtype)
reduced_L = K.T.astype(scipy_dtype) @ L_np.astype(scipy_dtype)
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K.astype(scipy_dtype) @ d
nt.assert_allclose(
uh_numpy.astype(u_mpc.dtype),
u_mpc,
rtol=500 * np.finfo(default_scalar_type).resolution,
)
list_timings(comm, [TimingType.wall])
@pytest.mark.parametrize("master_point", [[1, 1], [0, 1]])
def test_linearproblem(master_point):
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 3, 5)
V = fem.functionspace(mesh, ("Lagrange", 1))
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
d = fem.Constant(mesh, default_scalar_type(1.5))
c = fem.Constant(mesh, default_scalar_type(2))
x = ufl.SpatialCoordinate(mesh)
f = c * ufl.sin(2 * ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
g = fem.Function(V)
g.interpolate(lambda x: np.sin(x[0]) * x[1])
h = fem.Function(V)
h.interpolate(lambda x: 2 + x[1] * x[0])
a = d * g * ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
rhs = h * ufl.inner(f, v) * ufl.dx
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(fem.form(a))
A_org.assemble()
L_org = fem.petsc.assemble_vector(fem.form(rhs))
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
# Create multipoint constraint
def l2b(li):
return np.array(li, dtype=mesh.geometry.x.dtype).tobytes()
s_m_c = {
l2b([1, 0]): {l2b([0, 1]): 0.43, l2b([1, 1]): 0.11},
l2b([0, 0]): {l2b(master_point): 0.69},
}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
problem = dolfinx_mpc.LinearProblem(a, rhs, mpc, bcs=[], petsc_options={"ksp_type": "preonly", "pc_type": "lu"})
uh = problem.solve()
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
# Gather LHS, RHS and solution on one process
is_complex = np.issubdtype(default_scalar_type, np.complexfloating) # type: ignore
scipy_dtype = np.complex128 if is_complex else np.float64
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh.x.petsc_vec, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T.astype(scipy_dtype) * A_csr.astype(scipy_dtype) * K.astype(scipy_dtype)
reduced_L = K.T.astype(scipy_dtype) @ L_np.astype(scipy_dtype)
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K.astype(scipy_dtype) @ d
nt.assert_allclose(
uh_numpy.astype(u_mpc.dtype),
u_mpc,
rtol=500 * np.finfo(default_scalar_type).resolution,
)
list_timings(comm, [TimingType.wall])
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