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# Copyright (C) 2022 Nathan Sime
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier: MIT
from __future__ import annotations
from mpi4py import MPI
from petsc4py import PETSc
import basix
import dolfinx
import dolfinx.fem
import dolfinx.mesh
import numpy as np
import pytest
import ufl
import dolfinx_mpc
import dolfinx_mpc.utils
@pytest.mark.parametrize("cell_type", (dolfinx.cpp.mesh.CellType.triangle, dolfinx.cpp.mesh.CellType.quadrilateral))
@pytest.mark.parametrize("ghost_mode", (dolfinx.cpp.mesh.GhostMode.none, dolfinx.cpp.mesh.GhostMode.shared_facet))
def test_mixed_element(cell_type, ghost_mode):
N = 4
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, N, N, cell_type=cell_type, ghost_mode=ghost_mode)
# Inlet velocity Dirichlet BC
bc_facets = dolfinx.mesh.locate_entities_boundary(
mesh,
mesh.topology.dim - 1,
lambda x: np.isclose(x[0], 0.0, atol=500 * np.finfo(x.dtype).resolution),
)
other_facets = dolfinx.mesh.locate_entities_boundary(
mesh,
mesh.topology.dim - 1,
lambda x: np.isclose(x[0], 1.0, atol=500 * np.finfo(x.dtype).resolution),
)
arg_sort = np.argsort(other_facets)
mt = dolfinx.mesh.meshtags(mesh, mesh.topology.dim - 1, other_facets[arg_sort], np.full_like(other_facets, 1))
# Rotate the mesh to induce more interesting slip BCs
th = np.pi / 4.0
rot = np.array([[np.cos(th), -np.sin(th)], [np.sin(th), np.cos(th)]])
gdim = mesh.geometry.dim
mesh.geometry.x[:, :gdim] = (rot @ mesh.geometry.x[:, :gdim].T).T
# Create the function space
cellname = mesh.ufl_cell().cellname()
Ve = basix.ufl.element(
basix.ElementFamily.P, cellname, 2, shape=(mesh.geometry.dim,), dtype=dolfinx.default_real_type
)
Qe = basix.ufl.element(basix.ElementFamily.P, cellname, 1, dtype=dolfinx.default_real_type)
V = dolfinx.fem.functionspace(mesh, Ve)
Q = dolfinx.fem.functionspace(mesh, Qe)
W = dolfinx.fem.functionspace(mesh, basix.ufl.mixed_element([Ve, Qe]))
inlet_velocity = dolfinx.fem.Function(V)
inlet_velocity.interpolate(
lambda x: np.zeros((mesh.geometry.dim, x[0].shape[0]), dtype=dolfinx.default_scalar_type)
)
inlet_velocity.x.scatter_forward()
# -- Nested assembly
dofs = dolfinx.fem.locate_dofs_topological(V, 1, bc_facets)
bc1 = dolfinx.fem.dirichletbc(inlet_velocity, dofs)
# Collect Dirichlet boundary conditions
bcs = [bc1]
mpc_v = dolfinx_mpc.MultiPointConstraint(V)
n_approx = dolfinx_mpc.utils.create_normal_approximation(V, mt, 1)
mpc_v.create_slip_constraint(V, (mt, 1), n_approx, bcs=bcs)
mpc_v.finalize()
mpc_q = dolfinx_mpc.MultiPointConstraint(Q)
mpc_q.finalize()
f = dolfinx.fem.Constant(mesh, dolfinx.default_scalar_type((0, 0)))
(u, p) = ufl.TrialFunction(V), ufl.TrialFunction(Q)
(v, q) = ufl.TestFunction(V), ufl.TestFunction(Q)
a00 = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
a01 = -ufl.inner(p, ufl.div(v)) * ufl.dx
a10 = -ufl.inner(ufl.div(u), q) * ufl.dx
a11 = None
L0 = ufl.inner(f, v) * ufl.dx
L1 = ufl.inner(dolfinx.fem.Constant(mesh, dolfinx.default_scalar_type(0.0)), q) * ufl.dx
n = ufl.FacetNormal(mesh)
g_tau = ufl.as_vector((0.0, 0.0))
ds = ufl.Measure("ds", domain=mesh, subdomain_data=mt, subdomain_id=1)
a00 -= ufl.inner(ufl.outer(n, n) * ufl.dot(ufl.grad(u), n), v) * ds
a01 -= ufl.inner(ufl.outer(n, n) * ufl.dot(-p * ufl.Identity(u.ufl_shape[0]), n), v) * ds
L0 += ufl.inner(g_tau, v) * ds
a_nest = dolfinx.fem.form(((a00, a01), (a10, a11)))
L_nest = dolfinx.fem.form((L0, L1))
# Assemble MPC nest matrix
A_nest = dolfinx_mpc.create_matrix_nest(a_nest, [mpc_v, mpc_q])
dolfinx_mpc.assemble_matrix_nest(A_nest, a_nest, [mpc_v, mpc_q], bcs)
A_nest.assemble()
# Assemble original nest matrix
A_org_nest = dolfinx.fem.petsc.assemble_matrix_nest(a_nest, bcs)
A_org_nest.assemble()
# MPC nested rhs
b_nest = dolfinx_mpc.create_vector_nest(L_nest, [mpc_v, mpc_q])
dolfinx_mpc.assemble_vector_nest(b_nest, L_nest, [mpc_v, mpc_q])
dolfinx.fem.petsc.apply_lifting_nest(b_nest, a_nest, bcs)
for b_sub in b_nest.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
bcs0 = dolfinx.fem.bcs_by_block(dolfinx.fem.extract_function_spaces(L_nest), bcs)
dolfinx.fem.petsc.set_bc_nest(b_nest, bcs0)
# Original dolfinx rhs
b_org_nest = dolfinx.fem.petsc.assemble_vector_nest(L_nest)
dolfinx.fem.petsc.apply_lifting_nest(b_org_nest, a_nest, bcs)
for b_sub in b_org_nest.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc_nest(b_org_nest, bcs0)
# -- Monolithic assembly
dofs = dolfinx.fem.locate_dofs_topological((W.sub(0), V), 1, bc_facets)
bc1 = dolfinx.fem.dirichletbc(inlet_velocity, dofs, W.sub(0))
bcs = [bc1]
V, _ = W.sub(0).collapse()
mpc_vq = dolfinx_mpc.MultiPointConstraint(W)
n_approx = dolfinx_mpc.utils.create_normal_approximation(V, mt, 1)
mpc_vq.create_slip_constraint(W.sub(0), (mt, 1), n_approx, bcs=bcs)
mpc_vq.finalize()
f = dolfinx.fem.Constant(mesh, dolfinx.default_scalar_type((0, 0)))
(u, p) = ufl.TrialFunctions(W)
(v, q) = ufl.TestFunctions(W)
a = (
ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
- ufl.inner(p, ufl.div(v)) * ufl.dx
- ufl.inner(ufl.div(u), q) * ufl.dx
)
L = ufl.inner(f, v) * ufl.dx + ufl.inner(dolfinx.fem.Constant(mesh, dolfinx.default_scalar_type(0.0)), q) * ufl.dx
# No prescribed shear stress
n = ufl.FacetNormal(mesh)
g_tau = ufl.as_vector((0.0, 0.0))
ds = ufl.Measure("ds", domain=mesh, subdomain_data=mt, subdomain_id=1)
# Terms due to slip condition
# Explained in for instance: https://arxiv.org/pdf/2001.10639.pdf
a -= ufl.inner(ufl.outer(n, n) * ufl.dot(ufl.grad(u), n), v) * ds
a -= ufl.inner(ufl.outer(n, n) * ufl.dot(-p * ufl.Identity(u.ufl_shape[0]), n), v) * ds
L += ufl.inner(g_tau, v) * ds
a, L = dolfinx.fem.form(a), dolfinx.fem.form(L)
# Assemble LHS matrix and RHS vector
A = dolfinx_mpc.assemble_matrix(a, mpc_vq, bcs)
A.assemble()
A_org = dolfinx.fem.petsc.assemble_matrix(a, bcs)
A_org.assemble()
b = dolfinx_mpc.assemble_vector(L, mpc_vq)
b_org = dolfinx.fem.petsc.assemble_vector(L)
# Set Dirichlet boundary condition values in the RHS
dolfinx_mpc.apply_lifting(b, [a], [bcs], mpc_vq)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc(b, bcs)
dolfinx.fem.petsc.apply_lifting(b_org, [a], [bcs])
b_org.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc(b_org, bcs)
# -- Verification
def nest_matrix_norm(A):
assert A.getType() == "nest"
nrows, ncols = A.getNestSize()
sub_A = [A.getNestSubMatrix(row, col) for row in range(nrows) for col in range(ncols)]
return sum(map(lambda A_: A_.norm() ** 2 if A_ else 0.0, sub_A)) ** 0.5
# -- Ensure monolithic and nest matrices are the same
assert np.isclose(nest_matrix_norm(A_nest), A.norm())
for b_sub in b_nest.getNestSubVecs():
b_sub.destroy()
b_nest.destroy()
for b_sub in b_org_nest.getNestSubVecs():
b_sub.destroy()
b_org_nest.destroy()
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