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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 compute_midpoints, create_unit_square, meshtags
import dolfinx_mpc
from dolfinx_mpc.utils import get_assemblers # noqa: F401
@pytest.mark.parametrize("get_assemblers", ["C++"], indirect=True)
def test_cell_domains(get_assemblers): # noqa: F811
"""
Periodic MPC conditions over integral with different cell subdomains
"""
assemble_matrix, assemble_vector = get_assemblers
N = 5
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 15, N)
V = fem.functionspace(mesh, ("Lagrange", 1))
def left_side(x):
return x[0] < 0.5
tdim = mesh.topology.dim
num_cells = mesh.topology.index_map(tdim).size_local
cells = np.arange(num_cells, dtype=np.int32)
mesh.topology.create_connectivity(tdim, tdim)
cell_midpoints = compute_midpoints(mesh, tdim, cells)
values = np.ones_like(cells)
# All cells on right side marked one, all other with 1
values += left_side(cell_midpoints.T)
ct = meshtags(mesh, mesh.topology.dim, cells, values)
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
c1 = fem.Constant(mesh, default_scalar_type(2))
c2 = fem.Constant(mesh, default_scalar_type(10))
dx = ufl.Measure("dx", domain=mesh, subdomain_data=ct)
a = (
c1 * ufl.inner(ufl.grad(u), ufl.grad(v)) * dx(1)
+ c2 * ufl.inner(ufl.grad(u), ufl.grad(v)) * dx(2)
+ 0.87 * ufl.inner(u, v) * dx(1)
)
rhs = ufl.inner(x[1], v) * dx(1) + ufl.inner(fem.Constant(mesh, default_scalar_type(1)), v) * dx(2)
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)
def l2b(li):
return np.array(li, dtype=mesh.geometry.x.dtype).tobytes()
s_m_c = {}
for i in range(0, N + 1):
s_m_c[l2b([1, i / N])] = {l2b([0, i / N]): 1}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
# Setup MPC system
with Timer("~TEST: Assemble matrix old"):
A = assemble_matrix(bilinear_form, mpc)
with Timer("~TEST: Assemble vector"):
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)
pc = solver.getPC()
pc.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
is_complex = np.issubdtype(default_scalar_type, np.complexfloating) # type: ignore
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 (work with high precision )
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.astype(scipy_dtype), reduced_L.astype(scipy_dtype))
# Back substitution to full solution vector
uh_numpy = K.astype(scipy_dtype) @ d.astype(scipy_dtype)
nt.assert_allclose(
uh_numpy.astype(u_mpc.dtype),
u_mpc,
rtol=500 * np.finfo(default_scalar_type).resolution,
)
solver.destroy()
b.destroy()
A.destroy()
pc.destroy()
L_org.destroy()
A_org.destroy()
list_timings(comm, [TimingType.wall])
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