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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
import resource
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser
from pathlib import Path
from typing import Optional
from mpi4py import MPI
from petsc4py import PETSc
import basix.ufl
import h5py
import numpy as np
from dolfinx import default_real_type, default_scalar_type
from dolfinx.common import Timer, TimingType, list_timings
from dolfinx.fem import (
Constant,
Function,
dirichletbc,
form,
functionspace,
locate_dofs_topological,
set_bc,
)
from dolfinx.io import XDMFFile
from dolfinx.mesh import create_unit_cube, locate_entities_boundary, meshtags, refine
from ufl import Identity, TestFunction, TrialFunction, ds, dx, grad, inner, sym, tr
from dolfinx_mpc import MultiPointConstraint, apply_lifting, assemble_matrix, assemble_vector
from dolfinx_mpc.utils import log_info, rigid_motions_nullspace
def bench_elasticity_one(
r_lvl: int = 0,
out_hdf5: Optional[h5py.File] = None,
xdmf: bool = False,
boomeramg: bool = False,
kspview: bool = False,
):
N = 3
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N)
for i in range(r_lvl):
mesh.topology.create_entities(mesh.topology.dim - 2)
mesh = refine(mesh, redistribute=True)
fdim = mesh.topology.dim - 1
el = basix.ufl.element(
"Lagrange", mesh.topology.cell_name(), 1, shape=(mesh.geometry.dim,), dtype=default_real_type
)
V = functionspace(mesh, el)
# Generate Dirichlet BC on lower boundary (Fixed)
u_bc = Function(V)
with u_bc.x.petsc_vec.localForm() as u_local:
u_local.set(0.0)
u_bc.x.petsc_vec.destroy()
def boundaries(x):
return np.isclose(x[0], np.finfo(float).eps)
facets = locate_entities_boundary(mesh, fdim, boundaries)
topological_dofs = locate_dofs_topological(V, fdim, facets)
bc = dirichletbc(u_bc, topological_dofs)
bcs = [bc]
# Create traction meshtag
def traction_boundary(x):
return np.isclose(x[0], 1)
t_facets = locate_entities_boundary(mesh, fdim, traction_boundary)
facet_values = np.ones(len(t_facets), dtype=np.int32)
arg_sort = np.argsort(t_facets)
mt = meshtags(mesh, fdim, t_facets[arg_sort], facet_values[arg_sort])
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
# Elasticity parameters
E = 1.0e4
nu = 0.1
mu = Constant(mesh, default_scalar_type(E / (2.0 * (1.0 + nu))))
lmbda = Constant(mesh, default_scalar_type(E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))))
g = Constant(mesh, (0, 0, -1e2))
# 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)
a = inner(sigma(u), grad(v)) * dx
rhs = inner(g, v) * ds(domain=mesh, subdomain_data=mt, subdomain_id=1)
# Create MPC
with Timer("~Elasticity: Init constraint"):
def l2b(li):
return np.array(li, dtype=mesh.geometry.x.dtype).tobytes()
s_m_c = {l2b([1, 0, 0]): {l2b([1, 0, 1]): 0.5}}
mpc = MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c, 2, 2)
mpc.finalize()
# Setup MPC system
bilinear_form = form(a)
linear_form = form(rhs)
with Timer("~Elasticity: Assemble LHS and RHS"):
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
b = assemble_vector(linear_form, mpc)
# Apply boundary conditions
apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE) # type: ignore
set_bc(b, bcs)
# Create functionspace and function for mpc vector
# Solve Linear problem
solver = PETSc.KSP().create(mesh.comm) # type: ignore
opts = PETSc.Options() # type: ignore
if boomeramg:
opts["ksp_type"] = "cg"
opts["ksp_rtol"] = 1.0e-5
opts["pc_type"] = "hypre"
opts["pc_hypre_type"] = "boomeramg"
opts["pc_hypre_boomeramg_max_iter"] = 1
opts["pc_hypre_boomeramg_cycle_type"] = "v"
# opts["pc_hypre_boomeramg_print_statistics"] = 1
else:
opts["ksp_rtol"] = 1.0e-10
opts["pc_type"] = "gamg"
opts["pc_gamg_type"] = "agg"
opts["pc_gamg_coarse_eq_limit"] = 1000
opts["pc_gamg_sym_graph"] = True
opts["mg_levels_ksp_type"] = "chebyshev"
opts["mg_levels_pc_type"] = "jacobi"
opts["mg_levels_esteig_ksp_type"] = "cg"
opts["matptap_via"] = "scalable"
# opts["help"] = None # List all available options
# opts["ksp_view"] = None # List progress of solver
with Timer("~Elasticity: Solve problem") as timer:
null_space = rigid_motions_nullspace(mpc.function_space)
A.setNearNullSpace(null_space)
solver.setFromOptions()
solver.setOperators(A)
# Solve linear problem
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) # type: ignore
mpc.backsubstitution(uh)
solver_time = timer.elapsed()
it = solver.getIterationNumber()
if kspview:
solver.view()
# Print max usage of summary
mem = sum(MPI.COMM_WORLD.allgather(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss))
num_dofs = V.dofmap.index_map.size_global * V.dofmap.index_map_bs
if MPI.COMM_WORLD.rank == 0:
print(f"Rlvl {r_lvl}, Iterations {it}")
print(f"Rlvl {r_lvl}, Max usage {mem} (kb), #dofs {num_dofs}")
if out_hdf5 is not None:
d_set = out_hdf5.get("its")
d_set[r_lvl] = it
d_set = out_hdf5.get("num_dofs")
d_set[r_lvl] = num_dofs
d_set = out_hdf5.get("solve_time")
d_set[r_lvl, MPI.COMM_WORLD.rank] = solver_time[0]
if xdmf:
# Write solution to file
u_h = Function(mpc.function_space)
u_h.x.petsc_vec.setArray(uh.array)
u_h.name = "u_mpc"
outdir = Path("results")
outdir.mkdir(exist_ok=True, parents=True)
fname = outdir / f"bench_elasticity_{r_lvl}.xdmf"
with XDMFFile(mesh.comm, fname, "w") as outfile:
outfile.write_mesh(mesh)
outfile.write_function(u_h)
if __name__ == "__main__":
parser = ArgumentParser(formatter_class=ArgumentDefaultsHelpFormatter)
parser.add_argument("--nref", default=1, type=int, dest="n_ref", help="Number of spatial refinements")
parser.add_argument("--xdmf", action="store_true", dest="xdmf", help="XDMF-output of function (Default false)")
parser.add_argument("--timings", action="store_true", dest="timings", help="List timings (Default false)")
parser.add_argument("--kspview", action="store_true", dest="kspview", help="View PETSc progress")
parser.add_argument("-o", default="elasticity_one.hdf5", dest="hdf5", help="Name of HDF5 output file")
solver_parser = parser.add_mutually_exclusive_group(required=False)
solver_parser.add_argument(
"--boomeramg",
dest="boomeramg",
default=True,
action="store_true",
help="Use BoomerAMG preconditioner (Default)",
)
solver_parser.add_argument("--gamg", dest="boomeramg", action="store_false", help="Use PETSc GAMG preconditioner")
args = parser.parse_args()
N = args.n_ref + 1
# Setup hd5f output file
h5f = h5py.File(args.hdf5, "w", driver="mpio", comm=MPI.COMM_WORLD)
h5f.create_dataset("its", (N,), dtype=np.int32)
h5f.create_dataset("num_dofs", (N,), dtype=np.int32)
sd = h5f.create_dataset("solve_time", (N, MPI.COMM_WORLD.size), dtype=np.float64)
solver = "BoomerAMG" if args.boomeramg else "GAMG"
sd.attrs["solver"] = np.bytes_(solver)
# Loop over refinement levels
for i in range(N):
log_info(f"Run {i} in progress")
bench_elasticity_one(r_lvl=i, out_hdf5=h5f, xdmf=args.xdmf, boomeramg=args.boomeramg, kspview=args.kspview)
if args.timings and i == N - 1:
list_timings(MPI.COMM_WORLD, [TimingType.wall])
h5f.close()
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