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"""Unit tests for geometric multigrid via PETSc"""
# Copyright (C) 2016 Patrick E. Farrell and Garth N. Wells
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
from dolfin import *
import pytest
from dolfin_utils.test import (skip_if_not_PETSc,
skip_if_not_petsc4py,
pushpop_parameters)
@pytest.mark.skip # See https://bitbucket.org/fenics-project/dolfin/issues/938
@skip_if_not_petsc4py
def test_mg_solver_laplace(pushpop_parameters):
parameters["linear_algebra_backend"] = "PETSc"
# Create meshes and function spaces
meshes = [UnitSquareMesh(N, N) for N in [16, 32, 64]]
V = [FunctionSpace(mesh, "Lagrange", 1) for mesh in meshes]
# Create variational problem on fine grid
u, v = TrialFunction(V[-1]), TestFunction(V[-1])
a = dot(grad(u), grad(v))*dx
L = v*dx
bc = DirichletBC(V[-1], Constant(0.0), "on_boundary")
A, b = assemble_system(a, L, bc)
# Create collection of PETSc DM objects
dm_collection = PETScDMCollection(V)
# Create PETSc Krylov solver and set operator
solver = PETScKrylovSolver()
solver.set_operator(A)
# Set PETSc solver type
PETScOptions.set("ksp_type", "richardson")
PETScOptions.set("pc_type", "mg")
# Set PETSc MG type and levels
PETScOptions.set("pc_mg_levels", len(V))
PETScOptions.set("pc_mg_galerkin")
# Set smoother
PETScOptions.set("mg_levels_ksp_type", "chebyshev")
PETScOptions.set("mg_levels_pc_type", "jacobi")
# Set tolerance and monitor residual
PETScOptions.set("ksp_monitor_true_residual")
PETScOptions.set("ksp_atol", 1.0e-12)
PETScOptions.set("ksp_rtol", 1.0e-12)
solver.set_from_options()
# Get fine grid DM and attach fine grid DM to solver
solver.set_dm(dm_collection.get_dm(-1))
solver.set_dm_active(False)
# Solve
x = PETScVector()
solver.solve(x, b)
# Check multigrid solution against LU solver solution
solver = LUSolver(A)
x_lu = Vector()
solver.solve(x_lu, b)
assert round((x - x_lu).norm("l2"), 10) == 0
# Clear all PETSc options
from petsc4py import PETSc
opts = PETSc.Options()
for key in opts.getAll():
opts.delValue(key)
@skip_if_not_petsc4py
def xtest_mg_solver_stokes(pushpop_parameters):
parameters["linear_algebra_backend"] = "PETSc"
mesh0 = UnitCubeMesh(2, 2, 2)
mesh1 = UnitCubeMesh(4, 4, 4)
mesh2 = UnitCubeMesh(8, 8, 8)
Ve = VectorElement("CG", mesh0.ufl_cell(), 2)
Qe = FiniteElement("CG", mesh0.ufl_cell(), 1)
Ze = MixedElement([Ve, Qe])
Z0 = FunctionSpace(mesh0, Ze)
Z1 = FunctionSpace(mesh1, Ze)
Z2 = FunctionSpace(mesh2, Ze)
W = Z2
# Boundaries
def right(x, on_boundary): return x[0] > (1.0 - DOLFIN_EPS)
def left(x, on_boundary): return x[0] < DOLFIN_EPS
def top_bottom(x, on_boundary):
return x[1] > 1.0 - DOLFIN_EPS or x[1] < DOLFIN_EPS
# No-slip boundary condition for velocity
noslip = Constant((0.0, 0.0, 0.0))
bc0 = DirichletBC(W.sub(0), noslip, top_bottom)
# Inflow boundary condition for velocity
inflow = Expression(("-sin(x[1]*pi)", "0.0", "0.0"), degree=2)
bc1 = DirichletBC(W.sub(0), inflow, right)
# Collect boundary conditions
bcs = [bc0, bc1]
# Define variational problem
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
f = Constant((0.0, 0.0, 0.0))
a = inner(grad(u), grad(v))*dx + div(v)*p*dx + q*div(u)*dx
L = inner(f, v)*dx
# Form for use in constructing preconditioner matrix
b = inner(grad(u), grad(v))*dx + p*q*dx
# Assemble system
A, bb = assemble_system(a, L, bcs)
# Assemble preconditioner system
P, btmp = assemble_system(b, L, bcs)
spaces = [Z0, Z1, Z2]
dm_collection = PETScDMCollection(spaces)
solver = PETScKrylovSolver()
solver.set_operators(A, P)
PETScOptions.set("ksp_type", "gcr")
PETScOptions.set("pc_type", "mg")
PETScOptions.set("pc_mg_levels", 3)
PETScOptions.set("pc_mg_galerkin")
PETScOptions.set("ksp_monitor_true_residual")
PETScOptions.set("ksp_atol", 1.0e-10)
PETScOptions.set("ksp_rtol", 1.0e-10)
solver.set_from_options()
from petsc4py import PETSc
ksp = solver.ksp()
ksp.setDM(dm_collection.dm())
ksp.setDMActive(False)
x = PETScVector()
solver.solve(x, bb)
# Check multigrid solution against LU solver
solver = LUSolver(A)
x_lu = Vector()
solver.solve(x_lu, bb)
assert round((x - x_lu).norm("l2"), 10) == 0
# Clear all PETSc options
opts = PETSc.Options()
for key in opts.getAll():
opts.delValue(key)
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