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# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier: MIT
#
# Create constraint between two bodies that are not in contact
from __future__ import annotations
from pathlib import Path
from mpi4py import MPI
import gmsh
import numpy as np
from dolfinx import default_scalar_type
from dolfinx.fem import (
Constant,
Function,
FunctionSpace,
dirichletbc,
functionspace,
locate_dofs_geometrical,
locate_dofs_topological,
)
from dolfinx.io import XDMFFile, gmshio
from dolfinx.mesh import locate_entities_boundary
from ufl import (
Identity,
Measure,
SpatialCoordinate,
TestFunction,
TrialFunction,
grad,
inner,
sym,
tr,
)
from dolfinx_mpc import LinearProblem, MultiPointConstraint
from dolfinx_mpc.utils import create_point_to_point_constraint, rigid_motions_nullspace
# Mesh parameters for creating a mesh consisting of two disjoint rectangles
right_tag = 1
left_tag = 2
gmsh.initialize()
if MPI.COMM_WORLD.rank == 0:
gmsh.clear()
left_rectangle = gmsh.model.occ.addRectangle(0, 0, 0, 1, 1)
right_rectangle = gmsh.model.occ.addRectangle(1.1, 0, 0, 1, 1)
gmsh.model.occ.synchronize()
# Add physical tags for volumes
gmsh.model.addPhysicalGroup(2, [right_rectangle], tag=right_tag)
gmsh.model.setPhysicalName(2, right_tag, "Right square")
gmsh.model.addPhysicalGroup(2, [left_rectangle], tag=left_tag)
gmsh.model.setPhysicalName(2, left_tag, "Left square")
gmsh.option.setNumber("Mesh.CharacteristicLengthMin", 1)
gmsh.option.setNumber("Mesh.CharacteristicLengthMax", 1)
# Generate mesh
gmsh.model.mesh.generate(2)
# gmsh.option.setNumber("General.Terminal", 1)
gmsh.model.mesh.optimize("Netgen")
mesh, ct, _ = gmshio.model_to_mesh(gmsh.model, MPI.COMM_WORLD, 0, gdim=2)
gmsh.clear()
gmsh.finalize()
MPI.COMM_WORLD.barrier()
with XDMFFile(mesh.comm, "test.xdmf", "w") as xdmf:
xdmf.write_mesh(mesh)
V = functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,)))
tdim = mesh.topology.dim
fdim = tdim - 1
# Locate cells with different elasticity parameters
DG0 = functionspace(mesh, ("DG", 0))
mesh.topology.create_connectivity(tdim, tdim)
left_dofs = locate_dofs_topological(DG0, tdim, ct.find(left_tag))
right_dofs = locate_dofs_topological(DG0, tdim, ct.find(right_tag))
# Elasticity parameters
E_right = 1e2
E_left = 1e2
nu_right = 0.3
nu_left = 0.1
mu = Function(DG0)
lmbda = Function(DG0)
with mu.x.petsc_vec.localForm() as local:
local.array[left_dofs] = E_left / (2 * (1 + nu_left))
local.array[right_dofs] = E_right / (2 * (1 + nu_right))
with lmbda.x.petsc_vec.localForm() as local:
local.array[left_dofs] = E_left * nu_left / ((1 + nu_left) * (1 - 2 * nu_left))
local.array[right_dofs] = E_right * nu_right / ((1 + nu_right) * (1 - 2 * nu_right))
mu.x.petsc_vec.destroy()
lmbda.x.petsc_vec.destroy()
# Stress computation
def sigma(v):
return 2.0 * mu * sym(grad(v)) + lmbda * tr(sym(grad(v))) * Identity(len(v))
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
dx = Measure("dx", domain=mesh, subdomain_data=ct)
a = inner(sigma(u), grad(v)) * dx
x = SpatialCoordinate(mesh)
rhs = inner(Constant(mesh, default_scalar_type((0, 0))), v) * dx
# Set boundary conditions
u_push = np.array([0.1, 0], dtype=default_scalar_type)
dofs = locate_dofs_geometrical(V, lambda x: np.isclose(x[0], 0))
bc_push = dirichletbc(u_push, dofs, V)
u_fix = np.array([0, 0], dtype=default_scalar_type)
bc_fix = dirichletbc(u_fix, locate_dofs_geometrical(V, lambda x: np.isclose(x[0], 2.1)), V)
bcs = [bc_push, bc_fix]
def gather_dof_coordinates(V: FunctionSpace, dofs: np.ndarray):
"""
Distributes the dof coordinates of this subset of dofs to all processors
"""
x = V.tabulate_dof_coordinates()
local_dofs = dofs[dofs < V.dofmap.index_map.size_local * V.dofmap.index_map_bs]
coords = x[local_dofs]
num_nodes = len(coords)
glob_num_nodes = MPI.COMM_WORLD.allreduce(num_nodes, op=MPI.SUM)
recvbuf = np.empty(0, dtype=V.mesh.geometry.x.dtype)
if MPI.COMM_WORLD.rank == 0:
recvbuf = np.zeros(3 * glob_num_nodes, dtype=V.mesh.geometry.x.dtype)
sendbuf = coords.reshape(-1)
sendcounts = np.array(MPI.COMM_WORLD.gather(len(sendbuf), 0))
MPI.COMM_WORLD.Gatherv(sendbuf, (recvbuf, sendcounts), root=0) # type: ignore
glob_coords = MPI.COMM_WORLD.bcast(recvbuf, root=0).reshape((-1, 3))
return glob_coords
# Create pairs of dofs at each boundary
V0, _ = V.sub(0).collapse()
facets_r = locate_entities_boundary(mesh, fdim, lambda x: np.isclose(x[0], 1))
dofs_r = locate_dofs_topological(V0, fdim, facets_r)
facets_l = locate_entities_boundary(mesh, fdim, lambda x: np.isclose(x[0], 1.1))
dofs_l = locate_dofs_topological(V0, fdim, facets_l)
# Given the local coordinates of the dofs, distribute them on all processors
nodes = [gather_dof_coordinates(V0, dofs_r), gather_dof_coordinates(V0, dofs_l)]
pairs = []
for x in nodes[0]:
for y in nodes[1]:
if np.isclose(x[1], y[1]):
pairs.append([x, y])
break
mpc = MultiPointConstraint(V)
for i, pair in enumerate(pairs):
sl, ms, co, ow, off = create_point_to_point_constraint(V, pair[0], pair[1], vector=[1, 0])
mpc.add_constraint(V, sl, ms, co, ow, off)
mpc.finalize()
# Add back once PETSc release has added fix for
# https://gitlab.com/petsc/petsc/-/issues/1149
# petsc_options = {"ksp_rtol": 1.0e-8,
# "ksp_type": "cg",
# "pc_type": "gamg",
# "pc_gamg_type": "agg",
# "pc_gamg_coarse_eq_limit": 1000,
# "pc_gamg_sym_graph": True,
# "pc_gamg_square_graph": 2,
# "pc_gamg_threshold": 0.02,
# "mg_levels_ksp_type": "chebyshev",
# "mg_levels_pc_type": "jacobi",
# "mg_levels_esteig_ksp_type": "cg",
# # "matptap_via": "scalable",
# "ksp_view": None,
# "help": None,
# "ksp_monitor": None
# }
petsc_options = {"ksp_type": "preonly", "pc_type": "lu"}
problem = LinearProblem(a, rhs, mpc, bcs=bcs, petsc_options=petsc_options)
# Build near nullspace
null_space = rigid_motions_nullspace(mpc.function_space)
problem.A.setNearNullSpace(null_space)
u_h = problem.solve()
it = problem.solver.getIterationNumber()
unorm = u_h.x.petsc_vec.norm()
if MPI.COMM_WORLD.rank == 0:
print("Number of iterations: {0:d}".format(it))
# Write solution to file
u_h.name = "u"
outdir = Path("results")
outdir.mkdir(exist_ok=True, parents=True)
with XDMFFile(mesh.comm, outdir / "demo_elasticity_disconnect_2D.xdmf", "w") as xdmf:
xdmf.write_mesh(mesh)
xdmf.write_function(u_h)
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