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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 (create_unit_cube, locate_entities_boundary, meshtags,
refine)
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, TestFunction, TrialFunction, ds, dx, grad, inner,
sym, tr)
def bench_elasticity_one(r_lvl: int = 0, out_hdf5: 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
V = VectorFunctionSpace(mesh, ("Lagrange", 1))
# 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])
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
# Elasticity parameters
E = 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, (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=np.float64).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)
set_bc(b, bcs)
# Create functionspace and function for mpc vector
# Solve Linear problem
solver = PETSc.KSP().create(MPI.COMM_WORLD)
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-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)
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.vector.setArray(uh.array)
u_h.name = "u_mpc"
fname = f"results/bench_elasticity_{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=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.string_(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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