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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 pathlib import Path
from mpi4py import MPI
from petsc4py import PETSc
import dolfinx.fem as fem
import numpy as np
import scipy.sparse.linalg
from dolfinx import default_scalar_type
from dolfinx.common import Timer
from dolfinx.io import XDMFFile
from dolfinx.mesh import create_unit_square, locate_entities_boundary
from ufl import (
Identity,
SpatialCoordinate,
TestFunction,
TrialFunction,
as_vector,
dx,
grad,
inner,
sym,
tr,
)
import dolfinx_mpc.utils
from dolfinx_mpc import LinearProblem, MultiPointConstraint
def demo_elasticity():
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10)
V = fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,)))
# Generate Dirichlet BC on lower boundary (Fixed)
def boundaries(x):
return np.isclose(x[0], np.finfo(float).eps)
facets = locate_entities_boundary(mesh, 1, boundaries)
topological_dofs = fem.locate_dofs_topological(V, 1, facets)
bc = fem.dirichletbc(np.array([0, 0], dtype=default_scalar_type), topological_dofs, V)
bcs = [bc]
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
# Elasticity parameters
E = 1.0e4
nu = 0.0
mu = fem.Constant(mesh, default_scalar_type(E / (2.0 * (1.0 + nu))))
lmbda = fem.Constant(mesh, default_scalar_type(E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))))
# Stress computation
def sigma(v):
return 2.0 * mu * sym(grad(v)) + lmbda * tr(sym(grad(v))) * Identity(len(v))
x = SpatialCoordinate(mesh)
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
a = inner(sigma(u), grad(v)) * dx
rhs = inner(as_vector((0, (x[0] - 0.5) * 10**4 * x[1])), v) * dx
# Create MPC
def l2b(li):
return np.array(li, dtype=mesh.geometry.x.dtype).tobytes()
s_m_c = {l2b([1, 0]): {l2b([1, 1]): 0.9}}
mpc = MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c, 1, 1)
mpc.finalize()
# Solve Linear problem
petsc_options = {"ksp_type": "preonly", "pc_type": "lu"}
problem = LinearProblem(a, rhs, mpc, bcs=bcs, petsc_options=petsc_options)
u_h = problem.solve()
u_h.name = "u_mpc"
outdir = Path("results")
outdir.mkdir(exist_ok=True, parents=True)
with XDMFFile(mesh.comm, outdir / "demo_elasticity.xdmf", "w") as outfile:
outfile.write_mesh(mesh)
outfile.write_function(u_h)
# Solve the MPC problem using a global transformation matrix
# and numpy solvers to get reference values
bilinear_form = fem.form(a)
A_org = fem.petsc.assemble_matrix(bilinear_form, bcs)
A_org.assemble()
linear_form = fem.form(rhs)
L_org = fem.petsc.assemble_vector(linear_form)
fem.petsc.apply_lifting(L_org, [bilinear_form], [bcs])
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(L_org, bcs)
solver = PETSc.KSP().create(mesh.comm)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
solver.setOperators(A_org)
u_ = fem.Function(V)
solver.solve(L_org, u_.x.petsc_vec)
u_.x.scatter_forward()
u_.name = "u_unconstrained"
with XDMFFile(mesh.comm, outdir / "demo_elasticity.xdmf", "a") as outfile:
outfile.write_function(u_)
outfile.close()
root = 0
with Timer("~Demo: Verification"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, problem.A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, problem.b, mpc, root=root)
# Gather LHS, RHS and solution on one process
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(u_h.x.petsc_vec, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc, atol=500 * np.finfo(u_mpc.dtype).resolution)
# Print out master-slave connectivity for the first slave
master_owner = None
master_data = None
slave_owner = None
if mpc.num_local_slaves > 0:
slave_owner = MPI.COMM_WORLD.rank
bs = mpc.function_space.dofmap.index_map_bs
slave = mpc.slaves[0]
print("Constrained: {0:.5e}\n Unconstrained: {1:.5e}".format(u_h.x.array[slave], u_.x.petsc_vec.array[slave]))
master_owner = mpc._cpp_object.owners.links(slave)[0]
_masters = mpc.masters
master = _masters.links(slave)[0]
glob_master = mpc.function_space.dofmap.index_map.local_to_global(np.array([master // bs], dtype=np.int32))[0]
coeffs, offs = mpc.coefficients()
master_data = [glob_master * bs + master % bs, coeffs[offs[slave] : offs[slave + 1]][0]]
# If master not on proc send info to this processor
if MPI.COMM_WORLD.rank != master_owner:
MPI.COMM_WORLD.send(master_data, dest=master_owner, tag=1)
else:
print(
"Master*Coeff: {0:.5e}".format(
coeffs[offs[slave] : offs[slave + 1]][0] * u_h.x.array[_masters.links(slave)[0]]
)
)
# As a processor with a master is not aware that it has a master,
# Determine this so that it can receive the global dof and coefficient
master_recv = MPI.COMM_WORLD.allgather(master_owner)
for master in master_recv:
if master is not None:
master_owner = master
break
if slave_owner != master_owner and MPI.COMM_WORLD.rank == master_owner:
dofmap = mpc.function_space.dofmap
bs = dofmap.index_map_bs
in_data = MPI.COMM_WORLD.recv(source=MPI.ANY_SOURCE, tag=1)
num_local = dofmap.index_map.size_local + dofmap.index_map.num_ghosts
l2g = dofmap.index_map.local_to_global(np.arange(num_local, dtype=np.int32))
l_index = np.flatnonzero(l2g == in_data[0] // bs)[0]
print("Master*Coeff (on other proc): {0:.5e}".format(u_h.x.array[l_index * bs + in_data[0] % bs] * in_data[1]))
L_org.destroy()
solver.destroy()
if __name__ == "__main__":
demo_elasticity()
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