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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
from time import perf_counter
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)
from dolfinx.fem.petsc import (apply_lifting, assemble_matrix, assemble_vector,
set_bc)
from dolfinx.io import XDMFFile
from dolfinx.log import LogLevel, log, set_log_level
from dolfinx.mesh import (CellType, create_unit_cube, locate_entities_boundary,
meshtags, refine)
from dolfinx_mpc.utils import 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 ref_elasticity(tetra: bool = True, r_lvl: int = 0, out_hdf5: h5py.File = None,
xdmf: bool = False, boomeramg: bool = False, kspview: bool = False, degree: int = 1):
if tetra:
N = 3 if degree == 1 else 2
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N)
else:
N = 3
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, CellType.hexahedron)
for i in range(r_lvl):
# set_log_level(LogLevel.INFO)
N *= 2
if tetra:
mesh = refine(mesh, redistribute=True)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, CellType.hexahedron)
# set_log_level(LogLevel.ERROR)
N = degree * N
fdim = mesh.topology.dim - 1
V = VectorFunctionSpace(mesh, ("Lagrange", int(degree)))
# Generate Dirichlet BC on lower boundary (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)
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])
# 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(1e4)) * \
as_vector((0, -(x[2] - 0.5)**2, (x[1] - 0.5)**2))
# 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) + inner(f, v) * dx
num_dofs = V.dofmap.index_map.size_global * V.dofmap.index_map_bs
if MPI.COMM_WORLD.rank == 0:
print("Problem size {0:d} ".format(num_dofs))
# Generate reference matrices and unconstrained solution
bilinear_form = form(a)
A_org = assemble_matrix(bilinear_form, bcs)
A_org.assemble()
null_space_org = rigid_motions_nullspace(V)
A_org.setNearNullSpace(null_space_org)
linear_form = form(rhs)
L_org = assemble_vector(linear_form)
apply_lifting(L_org, [bilinear_form], [bcs])
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
set_bc(L_org, 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
# Create solver, set operator and options
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setFromOptions()
solver.setOperators(A_org)
# Solve linear problem
u_ = Function(V)
start = perf_counter()
with Timer("Ref solve"):
solver.solve(L_org, u_.vector)
end = perf_counter()
u_.x.scatter_forward()
if kspview:
solver.view()
it = solver.getIterationNumber()
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] = end - start
if MPI.COMM_WORLD.rank == 0:
print("Refinement level {0:d}, Iterations {1:d}".format(r_lvl, it))
# List memory usage
mem = sum(MPI.COMM_WORLD.allgather(
resource.getrusage(resource.RUSAGE_SELF).ru_maxrss))
if MPI.COMM_WORLD.rank == 0:
print("{1:d}: Max usage after trad. solve {0:d} (kb)"
.format(mem, r_lvl))
if xdmf:
# Name formatting of functions
u_.name = "u_unconstrained"
fname = "results/ref_elasticity_{0:d}.xdmf".format(r_lvl)
with XDMFFile(MPI.COMM_WORLD, fname, "w") as out_xdmf:
out_xdmf.write_mesh(mesh)
out_xdmf.write_function(u_, 0.0, "Xdmf/Domain/Grid[@Name='{0:s}'][1]".format(mesh.name))
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('--kspview', action='store_true', dest="kspview",
help="View PETSc progress")
parser.add_argument("-o", default='elasticity_ref.hdf5', dest="hdf5",
help="Name of HDF5 output file")
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
# 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"
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)
# Loop over refinement levels
for i in range(N):
if MPI.COMM_WORLD.rank == 0:
set_log_level(LogLevel.INFO)
log(LogLevel.INFO,
"Run {0:1d} in progress".format(i))
set_log_level(LogLevel.ERROR)
ref_elasticity(tetra=args.tetra, r_lvl=i, out_hdf5=h5f,
xdmf=args.xdmf, boomeramg=args.boomeramg, kspview=args.kspview,
degree=args.degree)
if args.timings and i == N - 1:
list_timings(MPI.COMM_WORLD, [TimingType.wall])
h5f.close()
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