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# This demo program solves Poisson's equation
#
# - div grad u(x, y) = f(x, y)
#
# on the unit square with homogeneous Dirichlet boundary conditions
# at y = 0, 1 and periodic boundary conditions at x = 0, 1.
#
# Copyright (C) Jørgen S. Dokken 2020.
#
# This file is part of DOLFINX_MPC.
#
# SPDX-License-Identifier: MIT
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser
import h5py
import numpy as np
from dolfinx.common import Timer, TimingType, list_timings
from dolfinx.fem import (Function, FunctionSpace, dirichletbc, form,
locate_dofs_geometrical, 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
from mpi4py import MPI
from petsc4py import PETSc
from ufl import (SpatialCoordinate, TestFunction, TrialFunction, dx, exp, grad,
inner, pi, sin)
def demo_periodic3D(tetra, r_lvl=0, out_hdf5=None,
xdmf=False, boomeramg=False, kspview=False, degree=1):
# Create mesh and function space
log_info(f"Run {r_lvl}: Create mesh")
ct = CellType.tetrahedron if tetra else CellType.hexahedron
# Tet setup
N = 3
for i in range(r_lvl):
N *= 2
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, ct)
V = FunctionSpace(mesh, ("CG", degree))
# Create Dirichlet boundary condition
def dirichletboundary(x):
return np.logical_or(np.logical_or(np.isclose(x[1], 0), np.isclose(x[1], 1)),
np.logical_or(np.isclose(x[2], 0), np.isclose(x[2], 1)))
mesh.topology.create_connectivity(2, 1)
geometrical_dofs = locate_dofs_geometrical(V, dirichletboundary)
bc = dirichletbc(PETSc.ScalarType(0), geometrical_dofs, V)
bcs = [bc]
def PeriodicBoundary(x):
return np.isclose(x[0], 1)
def periodic_relation(x):
out_x = np.zeros(x.shape)
out_x[0] = 1 - x[0]
out_x[1] = x[1]
out_x[2] = x[2]
return out_x
num_dofs = V.dofmap.index_map.size_global * V.dofmap.index_map_bs
log_info(f"Run {r_lvl}: Create MultiPoint Constraint {num_dofs}")
with Timer("~Periodic: Initialize periodic constraint"):
facets = locate_entities_boundary(mesh, mesh.topology.dim - 1, PeriodicBoundary)
arg_sort = np.argsort(facets)
mt = meshtags(mesh, mesh.topology.dim - 1, facets[arg_sort], np.full(len(facets), 2, dtype=np.int32))
mpc = MultiPointConstraint(V)
mpc.create_periodic_constraint_topological(V, mt, 2, periodic_relation, bcs)
mpc.finalize()
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v)) * dx
x = SpatialCoordinate(mesh)
dx_ = x[0] - 0.9
dy_ = x[1] - 0.5
dz_ = x[2] - 0.1
f = x[0] * sin(5.0 * pi * x[1]) + 1.0 * exp(-(dx_**2 + dy_**2 + dz_**2) / 0.02)
rhs = inner(f, v) * dx
# Assemble LHS and RHS with multi-point constraint
log_info(f"Run {r_lvl}: Assemble matrix")
bilinear_form = form(a)
with Timer(f"~Periodic {r_lvl}: Assemble matrix (cached)"):
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
log_info(f"Run {r_lvl}: Assembling vector")
linear_form = form(rhs)
with Timer(f"~Periodic: {r_lvl} Assemble vector (Total time)"):
b = assemble_vector(linear_form, mpc)
# Apply boundary conditions
log_info(f"Run {r_lvl}: Apply lifting")
apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
set_bc(b, bcs)
# Create nullspace
nullspace = PETSc.NullSpace().create(constant=True)
# Set PETSc solver options
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_type"] = "cg"
opts["ksp_rtol"] = 1.0e-12
opts["pc_type"] = "gamg"
opts["pc_gamg_type"] = "agg"
opts["pc_gamg_sym_graph"] = True
# Use Chebyshev smoothing for multigrid
opts["mg_levels_ksp_type"] = "richardson"
opts["mg_levels_pc_type"] = "sor"
# opts["help"] = None # List all available options
# opts["ksp_view"] = None # List progress of solver
# Solve linear problem
log_info(f"Run {r_lvl}: Solving")
solver = PETSc.KSP().create(MPI.COMM_WORLD)
with Timer("~Periodic: Solve") as timer:
# Create solver, set operator and options
PETSc.Mat.setNearNullSpace(A, nullspace)
uh = b.copy()
solver.setFromOptions()
solver.setOperators(A)
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()
# Output information to HDF5
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 MPI.COMM_WORLD.rank == 0:
print(f"Rlvl {r_lvl}, Iterations {it}")
# Output solution to XDMF
if xdmf:
# Create function space with correct index map for MPC
u_h = Function(mpc.function_space)
u_h.vector.setArray(uh.array)
# Name formatting of functions
ext = "tet" if tetra else "hex"
mesh.name = f"mesh_{ext}"
u_h.name = f"u_{ext}"
fname = f"results/bench_periodic3d_{r_lvl}_{ext}.xdmf"
with XDMFFile(MPI.COMM_WORLD, fname, "w") as out_xdmf:
out_xdmf.write_mesh(mesh)
out_xdmf.write_function(u_h, 0.0, f"Xdmf/Domain/Grid[@Name='{mesh.name}'][1]")
if __name__ == "__main__":
# Set Argparser defaults
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='periodic_output.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
# Prepare output HDF5 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)
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)
# Loop over refinements
for i in range(N):
log_info(f"Run {i} in progress")
demo_periodic3D(args.tetra, r_lvl=i, out_hdf5=h5f, xdmf=args.xdmf,
boomeramg=args.boomeramg, kspview=args.kspview, degree=int(args.degree))
# List_timings
if args.timings and i == N - 1:
list_timings(MPI.COMM_WORLD, [TimingType.wall])
h5f.close()
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