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# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier: MIT
#
# Multi point constraint problem for linear elasticity with slip conditions
# between two cubes.
from __future__ import annotations
from mpi4py import MPI
from petsc4py import PETSc
import dolfinx.fem as fem
import gmsh
import numpy as np
import numpy.testing as nt
import pytest
import scipy.sparse.linalg
import ufl
from dolfinx import default_scalar_type
from dolfinx.common import Timer, TimingType, list_timings
from dolfinx.io import gmshio
import dolfinx_mpc
import dolfinx_mpc.utils
from dolfinx_mpc.utils import get_assemblers # noqa: F401
theta = np.pi / 5
@pytest.fixture
def generate_hex_boxes():
"""
Generate the stacked boxes [x0,y0,z0]x[y1,y1,z1] and
[x0,y0,z1] x [x1,y1,z2] with different resolution in each box.
The markers are is a list of arrays containing markers
array of markers for [back, bottom, right, left, top, front] per box
volume_markers a list of marker per volume
"""
res = 0.2
x0, y0, z0, x1, y1, z1, z2 = 0, 0, 0, 1, 1, 1, 2
facet_markers = [[11, 5, 12, 13, 4, 14], [21, 9, 22, 23, 3, 24]]
volume_markers = [1, 2]
r_matrix = dolfinx_mpc.utils.rotation_matrix([1, 1, 0], -theta)
# Check if GMSH is initialized
gmsh.initialize()
gmsh.clear()
if MPI.COMM_WORLD.rank == 0:
gmsh.option.setNumber("Mesh.RecombinationAlgorithm", 2)
gmsh.option.setNumber("Mesh.RecombineAll", 2)
gmsh.option.setNumber("General.Terminal", 0)
bottom = gmsh.model.occ.addRectangle(x0, y0, z0, x1 - x0, y1 - y0)
top = gmsh.model.occ.addRectangle(x0, y0, z2, x1 - x0, y1 - y0)
# Set mesh size at point
gmsh.model.occ.extrude([(2, bottom)], 0, 0, z1 - z0, numElements=[int(1 / (2 * res))], recombine=True)
gmsh.model.occ.extrude([(2, top)], 0, 0, z1 - z2 - 1e-12, numElements=[int(1 / (2 * res))], recombine=True)
# Syncronize to be able to fetch entities
gmsh.model.occ.synchronize()
# Create entity -> marker map (to be used after rotation)
volumes = gmsh.model.getEntities(3)
volume_entities = {"Top": [None, volume_markers[1]], "Bottom": [None, volume_markers[0]]}
for i, volume in enumerate(volumes):
com = gmsh.model.occ.getCenterOfMass(volume[0], volume[1])
if np.isclose(com[2], (z1 - z0) / 2):
bottom_index = i
volume_entities["Bottom"][0] = volume
elif np.isclose(com[2], (z2 - z1) / 2 + z1):
top_index = i
volume_entities["Top"][0] = volume
surfaces = ["Top", "Bottom", "Left", "Right", "Front", "Back"]
entities = {
"Bottom": {key: [[], None] for key in surfaces},
"Top": {key: [[], None] for key in surfaces},
}
# Identitfy entities for each surface of top and bottom cube
# Physical markers for bottom cube
bottom_surfaces = gmsh.model.getBoundary([volumes[bottom_index]], recursive=False, oriented=False)
for entity in bottom_surfaces:
com = gmsh.model.occ.getCenterOfMass(entity[0], entity[1])
if np.allclose(com, [(x1 - x0) / 2, y1, (z1 - z0) / 2]):
entities["Bottom"]["Back"][0].append(entity[1])
entities["Bottom"]["Back"][1] = facet_markers[0][0]
elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z0]):
entities["Bottom"]["Bottom"][0].append(entity[1])
entities["Bottom"]["Bottom"][1] = facet_markers[0][1]
elif np.allclose(com, [x1, (y1 - y0) / 2, (z1 - z0) / 2]):
entities["Bottom"]["Right"][0].append(entity[1])
entities["Bottom"]["Right"][1] = facet_markers[0][2]
elif np.allclose(com, [x0, (y1 - y0) / 2, (z1 - z0) / 2]):
entities["Bottom"]["Left"][0].append(entity[1])
entities["Bottom"]["Left"][1] = facet_markers[0][3]
elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z1]):
entities["Bottom"]["Top"][0].append(entity[1])
entities["Bottom"]["Top"][1] = facet_markers[0][4]
elif np.allclose(com, [(x1 - x0) / 2, y0, (z1 - z0) / 2]):
entities["Bottom"]["Front"][0].append(entity[1])
entities["Bottom"]["Front"][1] = facet_markers[0][5]
# Physical markers for top
top_surfaces = gmsh.model.getBoundary([volumes[top_index]], recursive=False, oriented=False)
for entity in top_surfaces:
com = gmsh.model.occ.getCenterOfMass(entity[0], entity[1])
if np.allclose(com, [(x1 - x0) / 2, y1, (z2 - z1) / 2 + z1]):
entities["Top"]["Back"][0].append(entity[1])
entities["Top"]["Back"][1] = facet_markers[1][0]
elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z1]):
entities["Top"]["Bottom"][0].append(entity[1])
entities["Top"]["Bottom"][1] = facet_markers[1][1]
elif np.allclose(com, [x1, (y1 - y0) / 2, (z2 - z1) / 2 + z1]):
entities["Top"]["Right"][0].append(entity[1])
entities["Top"]["Right"][1] = facet_markers[1][2]
elif np.allclose(com, [x0, (y1 - y0) / 2, (z2 - z1) / 2 + z1]):
entities["Top"]["Left"][0].append(entity[1])
entities["Top"]["Left"][1] = facet_markers[1][3]
elif np.allclose(com, [(x1 - x0) / 2, (y1 - y0) / 2, z2]):
entities["Top"]["Top"][0].append(entity[1])
entities["Top"]["Top"][1] = facet_markers[1][4]
elif np.allclose(com, [(x1 - x0) / 2, y0, (z2 - z1) / 2 + z1]):
entities["Top"]["Front"][0].append(entity[1])
entities["Top"]["Front"][1] = facet_markers[1][5]
# gmsh.model.occ.rotate(volumes, 0, 0, 0,
# 1 / np.sqrt(2), 1 / np.sqrt(2), 0, theta)
# Note: Rotation cannot be used on recombined surfaces
gmsh.model.occ.synchronize()
for volume in volume_entities.keys():
gmsh.model.addPhysicalGroup(
volume_entities[volume][0][0],
[volume_entities[volume][0][1]],
tag=volume_entities[volume][1],
)
gmsh.model.setPhysicalName(volume_entities[volume][0][0], volume_entities[volume][1], volume)
for box in entities.keys():
for surface in entities[box].keys():
gmsh.model.addPhysicalGroup(2, entities[box][surface][0], tag=entities[box][surface][1])
gmsh.model.setPhysicalName(2, entities[box][surface][1], box + ":" + surface)
# Set mesh sizes on the points from the surface we are extruding
bottom_nodes = gmsh.model.getBoundary([(2, bottom)], recursive=True, oriented=False)
gmsh.model.occ.mesh.setSize(bottom_nodes, res)
top_nodes = gmsh.model.getBoundary([(2, top)], recursive=True, oriented=False)
gmsh.model.occ.mesh.setSize(top_nodes, 2 * res)
# NOTE: Need to synchronize after setting mesh sizes
gmsh.model.occ.synchronize()
# Generate mesh
gmsh.option.setNumber("Mesh.MaxNumThreads1D", MPI.COMM_WORLD.size)
gmsh.option.setNumber("Mesh.MaxNumThreads2D", MPI.COMM_WORLD.size)
gmsh.option.setNumber("Mesh.MaxNumThreads3D", MPI.COMM_WORLD.size)
gmsh.model.mesh.generate(3)
gmsh.model.mesh.setOrder(1)
mesh, _, ft = gmshio.model_to_mesh(gmsh.model, MPI.COMM_WORLD, 0)
gmsh.clear()
gmsh.finalize()
# NOTE: Hex mesh must be rotated after generation due to gmsh API
mesh.geometry.x[:] = np.dot(r_matrix, mesh.geometry.x.T).T
return (mesh, ft)
@pytest.mark.parametrize("get_assemblers", ["C++"], indirect=True)
@pytest.mark.parametrize("nonslip", [True, False])
def test_cube_contact(generate_hex_boxes, nonslip, get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
comm = MPI.COMM_WORLD
root = 0
# Generate mesh
mesh_data = generate_hex_boxes
mesh, mt = mesh_data
fdim = mesh.topology.dim - 1
# Create functionspaces
V = fem.functionspace(mesh, ("Lagrange", 1, (mesh.geometry.dim,)))
# Helper for orienting traction
# Bottom boundary is fixed in all directions
u_bc = fem.Function(V)
with u_bc.x.petsc_vec.localForm() as u_local:
u_local.set(0.0)
u_bc.x.petsc_vec.destroy()
bottom_dofs = fem.locate_dofs_topological(V, fdim, mt.find(5))
bc_bottom = fem.dirichletbc(u_bc, bottom_dofs)
g_vec = [0, 0, -4.25e-1]
if not nonslip:
# Helper for orienting traction
r_matrix = dolfinx_mpc.utils.rotation_matrix([1 / np.sqrt(2), 1 / np.sqrt(2), 0], -theta)
# Top boundary has a given deformation normal to the interface
g_vec = np.dot(r_matrix, [0, 0, -4.25e-1])
# Top boundary has a given deformation normal to the interface
def top_v(x):
values = np.empty((3, x.shape[1]))
values[0] = g_vec[0]
values[1] = g_vec[1]
values[2] = g_vec[2]
return values
u_top = fem.Function(V)
u_top.interpolate(top_v)
top_dofs = fem.locate_dofs_topological(V, fdim, mt.find(3))
bc_top = fem.dirichletbc(u_top, top_dofs)
bcs = [bc_bottom, bc_top]
# Elasticity parameters
E = 1.0e3
nu = 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 * ufl.sym(ufl.grad(v)) + lmbda * ufl.tr(ufl.sym(ufl.grad(v))) * ufl.Identity(len(v))
# Define variational problem
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(sigma(u), ufl.grad(v)) * ufl.dx
rhs = ufl.inner(fem.Constant(mesh, default_scalar_type((0, 0, 0))), v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Create LU solver
solver = PETSc.KSP().create(comm)
solver.setType("preonly")
solver.setTolerances(rtol=1.0e-14)
solver.getPC().setType("lu")
# Create MPC contact condition and assemble matrices
mpc = dolfinx_mpc.MultiPointConstraint(V)
if nonslip:
with Timer("~Contact: Create non-elastic constraint"):
mpc.create_contact_inelastic_condition(mt, 4, 9, eps2=500 * np.finfo(default_scalar_type).resolution)
else:
with Timer("~Contact: Create contact constraint"):
nh = dolfinx_mpc.utils.create_normal_approximation(V, mt, 4)
mpc.create_contact_slip_condition(mt, 4, 9, nh, eps2=500 * np.finfo(default_scalar_type).resolution)
mpc.finalize()
with Timer("~TEST: Assemble bilinear form"):
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
with Timer("~TEST: Assemble vector"):
b = assemble_vector(linear_form, mpc)
dolfinx_mpc.apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(b, bcs)
with Timer("~MPC: Solve"):
solver.setOperators(A)
uh = fem.Function(mpc.function_space)
uh.x.array[:] = 0
u_vec = uh.x.petsc_vec
solver.solve(b, u_vec)
u_vec.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
# Solve the MPC problem using a global transformation matrix
# and numpy solvers to get reference values
dolfinx_mpc.utils.log_info("Solving reference problem with global matrix (using numpy)")
with Timer("~TEST: Assemble bilinear form (unconstrained)"):
A_org = fem.petsc.assemble_matrix(bilinear_form, bcs)
A_org.assemble()
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)
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
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_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
atol = 1000 * np.finfo(default_scalar_type).resolution
nt.assert_allclose(uh_numpy, u_mpc, atol=atol)
L_org.destroy()
b.destroy()
solver.destroy()
list_timings(comm, [TimingType.wall])
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