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# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier: MIT
import resource
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser
import h5py
import numpy as np
from dolfinx.common import Timer, TimingType, list_timings
from dolfinx.fem import (Constant, Function, VectorFunctionSpace, dirichletbc,
form, locate_dofs_topological, set_bc)
from dolfinx.io import XDMFFile
from dolfinx.mesh import (CellType, create_unit_cube, locate_entities_boundary,
meshtags)
from dolfinx_mpc import (MultiPointConstraint, apply_lifting, assemble_matrix,
assemble_vector)
from dolfinx_mpc.utils import log_info, rigid_motions_nullspace
from mpi4py import MPI
from petsc4py import PETSc
from ufl import (Identity, SpatialCoordinate, TestFunction, TrialFunction,
as_vector, ds, dx, grad, inner, sym, tr)
def bench_elasticity_edge(tetra: bool = True, r_lvl: int = 0, out_hdf5=None, xdmf: bool = False,
boomeramg: bool = False, kspview: bool = False, degree: int = 1, info: bool = False):
N = 3
for i in range(r_lvl):
N *= 2
ct = CellType.tetrahedron if tetra else CellType.hexahedron
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, ct)
# Get number of unknowns on each edge
V = VectorFunctionSpace(mesh, ("Lagrange", int(degree)))
# Generate Dirichlet BC (Fixed)
u_bc = Function(V)
with u_bc.vector.localForm() as u_local:
u_local.set(0.0)
def boundaries(x):
return np.isclose(x[0], np.finfo(float).eps)
fdim = mesh.topology.dim - 1
facets = locate_entities_boundary(mesh, fdim, boundaries)
topological_dofs = locate_dofs_topological(V, fdim, facets)
bc = dirichletbc(u_bc, topological_dofs)
bcs = [bc]
def PeriodicBoundary(x):
return np.logical_and(np.isclose(x[0], 1), np.isclose(x[2], 0))
def periodic_relation(x):
out_x = np.zeros(x.shape)
out_x[0] = x[0]
out_x[1] = x[1]
out_x[2] = x[2] + 1
return out_x
with Timer("~Elasticity: Initialize MPC"):
edim = mesh.topology.dim - 2
edges = locate_entities_boundary(mesh, edim, PeriodicBoundary)
arg_sort = np.argsort(edges)
periodic_mt = meshtags(mesh, edim, edges[arg_sort], np.full(len(edges), 2, dtype=np.int32))
mpc = MultiPointConstraint(V)
mpc.create_periodic_constraint_topological(V, periodic_mt, 2, periodic_relation, bcs, scale=0.5)
mpc.finalize()
# 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)
# Elasticity parameters
E = PETSc.ScalarType(1.0e4)
nu = 0.1
mu = Constant(mesh, E / (2.0 * (1.0 + nu)))
lmbda = Constant(mesh, E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu)))
g = Constant(mesh, PETSc.ScalarType((0, 0, -1e2)))
x = SpatialCoordinate(mesh)
f = Constant(mesh, PETSc.ScalarType(1e3)) * as_vector((0, -(x[2] - 0.5)**2, (x[1] - 0.5)**2))
# Stress computation
def epsilon(v):
return sym(grad(v))
def sigma(v):
return (2.0 * mu * epsilon(v) + lmbda * tr(epsilon(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) + inner(f, v) * dx
# Setup MPC system
if info:
log_info(f"Run {r_lvl}: Assembling matrix and vector")
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)
# Create nullspace for elasticity problem and assign to matrix
null_space = rigid_motions_nullspace(mpc.function_space)
A.setNearNullSpace(null_space)
# Apply boundary conditions
apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
set_bc(b, bcs)
opts = PETSc.Options()
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-8
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["pc_gamg_square_graph"] = 2
opts["pc_gamg_threshold"] = 0.02
# opts["help"] = None # List all available options
# opts["ksp_view"] = None # List progress of solver
# Setup PETSc solver
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setFromOptions()
if info:
log_info(f"Run {r_lvl}: Solving")
with Timer("~Elasticity: Solve problem") as timer:
solver.setOperators(A)
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
solver_time = timer.elapsed()
if kspview:
solver.view()
mem = sum(MPI.COMM_WORLD.allgather(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss))
it = solver.getIterationNumber()
num_dofs = V.dofmap.index_map.size_global * V.dofmap.index_map_bs
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("num_slaves")
d_set[r_lvl, MPI.COMM_WORLD.rank] = mpc.num_local_slaves
d_set = out_hdf5.get("solve_time")
d_set[r_lvl, MPI.COMM_WORLD.rank] = solver_time[0]
if info:
log_info(f"Lvl: {r_lvl}, Its: {it}, max Mem: {mem}, dim(V): {num_dofs}")
if xdmf:
# Write solution to file
u_h = Function(mpc.function_space)
u_h.vector.setArray(uh.array)
u_h.name = "u_mpc"
fname = f"results/bench_elasticity_edge_{r_lvl}.xdmf"
with XDMFFile(MPI.COMM_WORLD, 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=np.int8, dest="n_ref", help="Number of spatial refinements")
parser.add_argument("--degree", default=1, type=np.int8, dest="degree", help="CG Function space degree")
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('--info', action='store_true', dest="info",
help="Set loglevel to info (Default false)", default=False)
parser.add_argument('--kspview', action='store_true', dest="kspview", help="View PETSc progress")
ct_parser = parser.add_mutually_exclusive_group(required=False)
ct_parser.add_argument('--tet', dest='tetra', action='store_true', help="Tetrahedron elements")
ct_parser.add_argument('--hex', dest='tetra', action='store_false', help="Hexahedron elements")
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
h5f = h5py.File('bench_edge_output.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)
h5f.create_dataset("num_slaves", (N, MPI.COMM_WORLD.size), dtype=np.int32)
sd = h5f.create_dataset("solve_time", (N, MPI.COMM_WORLD.size), dtype=np.float64)
solver = "BoomerAMG" if args.boomeramg else "GAMG"
ct = "Tet" if args.tetra else "Hex"
sd.attrs["solver"] = np.string_(solver)
sd.attrs["degree"] = np.string_(str(int(args.degree)))
sd.attrs["ct"] = np.string_(ct)
for i in range(N):
log_info(f"Run {i} in progress")
bench_elasticity_edge(tetra=args.tetra, r_lvl=i, out_hdf5=h5f, xdmf=args.xdmf,
boomeramg=args.boomeramg, kspview=args.kspview,
degree=args.degree, info=args.info)
if args.timings and i == N - 1:
list_timings(MPI.COMM_WORLD, [TimingType.wall])
h5f.close()
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