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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.
#
# Original implementation in DOLFIN by Kristian B. Oelgaard and Anders Logg
# This implementation can be found at:
# https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/documented/periodic/demo_periodic.py
#
# Copyright (C) Jørgen S. Dokken 2020.
#
# This file is part of DOLFINX_MPC.
#
# SPDX-License-Identifier: MIT
from __future__ import annotations
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser
from pathlib import Path
from time import perf_counter
from typing import Optional
from mpi4py import MPI
from petsc4py import PETSc
import h5py
import numpy as np
from dolfinx import default_scalar_type
from dolfinx.common import Timer, TimingType, list_timings
from dolfinx.fem import Function, dirichletbc, form, functionspace, locate_dofs_geometrical
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, refine
from ufl import SpatialCoordinate, TestFunction, TrialFunction, dx, exp, grad, inner, pi, sin
def reference_periodic(
tetra: bool,
r_lvl: int = 0,
out_hdf5: Optional[h5py.File] = None,
xdmf: bool = False,
boomeramg: bool = False,
kspview: bool = False,
degree: int = 1,
):
# Create mesh and finite element
if tetra:
# Tet setup
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)
N *= 2
else:
# Hex setup
N = 3
for i in range(r_lvl):
N *= 2
mesh = create_unit_cube(MPI.COMM_WORLD, N, N, N, CellType.hexahedron)
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(default_scalar_type(0), geometrical_dofs, V)
bcs = [bc]
# 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_ * dx_ + dy_ * dy_ + dz_ * dz_) / 0.02)
rhs = inner(f, v) * dx
# Assemble rhs, RHS and apply lifting
bilinear_form = form(a)
linear_form = form(rhs)
A_org = assemble_matrix(bilinear_form, bcs)
A_org.assemble()
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) # type: ignore
set_bc(L_org, bcs)
# Create PETSc nullspace
nullspace = PETSc.NullSpace().create(constant=True) # type: ignore
PETSc.Mat.setNearNullSpace(A_org, nullspace) # type: ignore
# Set PETSc options
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_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
# Initialize PETSc solver, set options and operator
solver = PETSc.KSP().create(mesh.comm) # type: ignore
solver.setFromOptions()
solver.setOperators(A_org)
# Solve linear problem
u_ = Function(V)
start = perf_counter()
with Timer("Solve"):
solver.solve(L_org, u_.x.petsc_vec)
end = perf_counter()
u_.x.petsc_vec.ghostUpdate(
addv=PETSc.InsertMode.INSERT, # type: ignore
mode=PETSc.ScatterMode.FORWARD, # type: ignore
) # type: ignore
if kspview:
solver.view()
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("solve_time")
d_set[r_lvl, MPI.COMM_WORLD.rank] = end - start
if MPI.COMM_WORLD.rank == 0:
print("Rlvl {0:d}, Iterations {1:d}".format(r_lvl, it))
# Output solution to XDMF
if xdmf:
ext = "tet" if tetra else "hex"
outdir = Path("results")
outdir.mkdir(exist_ok=True, parents=True)
fname = outdir / "reference_periodic_{0:d}_{1:s}.xdmf".format(r_lvl, ext)
u_.name = "u_" + ext + "_unconstrained"
with XDMFFile(mesh.comm, fname, "w") as out_periodic:
out_periodic.write_mesh(mesh)
out_periodic.write_function(u_, 0.0, "Xdmf/Domain/" + "Grid[@Name='{0:s}'][1]".format(mesh.name))
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_ref_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", default=True)
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("periodic_ref_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)
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.bytes_(solver)
sd.attrs["degree"] = np.bytes_(str(int(args.degree)))
sd.attrs["ct"] = np.bytes_(ct)
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)
reference_periodic(
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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