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"""Unit tests for LocalSolver"""
# Copyright (C) 2013 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/>.
#
# Modified by Steven Vandekerckhove, 2014
# Modified by Tormod Landet, 2015
import pytest
import numpy
from dolfin import *
from dolfin_utils.test import skip_in_parallel
from dolfin_utils.test import set_parameters_fixture
ghost_mode = set_parameters_fixture("ghost_mode", ["shared_facet"])
def test_solve_global_rhs():
mesh = UnitCubeMesh(2, 3, 3)
V = FunctionSpace(mesh, "Discontinuous Lagrange", 2)
W = FunctionSpace(mesh, "Lagrange", 2)
u, v = TrialFunction(V), TestFunction(V)
f = Expression("x[0]*x[0] + x[0]*x[1] + x[1]*x[1]", element=W.ufl_element())
# Forms for projection
a, L = inner(v, u)*dx, inner(v, f)*dx
solvers = [LocalSolver.SolverType.LU, LocalSolver.SolverType.Cholesky]
for solver_type in solvers:
# First solve
u = Function(V)
local_solver = LocalSolver(a, L, solver_type)
local_solver.solve_global_rhs(u)
error = assemble((u - f)*(u - f)*dx)
assert round(error, 10) == 0
# Test cached factorization
u.vector().zero()
local_solver.factorize()
local_solver.solve_global_rhs(u)
error = assemble((u - f)*(u - f)*dx)
assert round(error, 10) == 0
# Clear cache and re-compute
u.vector().zero()
local_solver.clear_factorization()
local_solver.solve_global_rhs(u)
error = assemble((u - f)*(u - f)*dx)
assert round(error, 10) == 0
def test_solve_local_rhs(ghost_mode):
mesh = UnitCubeMesh(1, 5, 1)
V = FunctionSpace(mesh, "Lagrange", 2)
W = FunctionSpace(mesh, "Lagrange", 2)
u, v = TrialFunction(V), TestFunction(V)
f = Constant(10.0)
# Forms for projection
a, L = inner(v, u)*dx, inner(v, f)*dx
solvers = [LocalSolver.SolverType.LU, LocalSolver.SolverType.Cholesky]
for solver_type in solvers:
# First solve
u = Function(V)
local_solver = LocalSolver(a, L, solver_type)
local_solver.solve_local_rhs(u)
x = u.vector().copy()
x[:] = 10.0
assert round((u.vector() - x).norm("l2") - 0.0, 10) == 0
u.vector().zero()
local_solver.factorize()
local_solver.solve_local_rhs(u)
assert round((u.vector() - x).norm("l2") - 0.0, 10) == 0
u.vector().zero()
local_solver.clear_factorization()
local_solver.solve_local_rhs(u)
assert round((u.vector() - x).norm("l2") - 0.0, 10) == 0
def test_solve_local_rhs_facet_integrals(ghost_mode):
mesh = UnitSquareMesh(4, 4)
# Facet function is used here to verify that the proper domains
# of the rhs are used unlike before where the rhs domains were
# taken to be the same as the lhs domains
marker = MeshFunction("size_t", mesh, mesh.topology().dim()-1, 0)
ds0 = Measure("ds", domain=mesh, subdomain_data=marker, subdomain_id=0)
Vu = VectorFunctionSpace(mesh, 'DG', 1)
Vv = FunctionSpace(mesh, 'DGT', 1)
u = TrialFunction(Vu)
v = TestFunction(Vv)
n = FacetNormal(mesh)
w = Constant([1, 1])
a = dot(u, n)*v*ds
L = dot(w, n)*v*ds0
for R in '+-':
a += dot(u(R), n(R))*v(R)*dS
L += dot(w(R), n(R))*v(R)*dS
u = Function(Vu)
local_solver = LocalSolver(a, L)
local_solver.solve_local_rhs(u)
x = u.vector().copy()
x[:] = 1
assert round((u.vector() - x).norm('l2'), 10) == 0
def test_local_solver_dg(ghost_mode):
mesh = UnitIntervalMesh(50)
U = FunctionSpace(mesh, "DG", 2)
# Set initial values
u0 = interpolate(Expression("cos(pi*x[0])", degree=2), U)
# Define test and trial functions
v, u = TestFunction(U), TrialFunction(U)
# Set time step size
dt = Constant(2.0e-4)
# Define fluxes on interior and exterior facets
u_hat = avg(u0) + 0.25*jump(u0)
u_hatbnd = -u0 + 0.25*(u0 - 1.0)
# Define variational formulation
a = u*v*dx
L = (u0*v + dt*u0*v.dx(0))*dx - dt*u_hat*jump(v)*dS - dt*u_hatbnd*v*ds
# Compute reference solution with global LU solver
u_lu = Function(U)
solve(a == L, u_lu, solver_parameters = {"linear_solver" : "lu"})
# Compute solution with local solver and compare
local_solver = LocalSolver(a, L)
u_ls = Function(U)
local_solver.solve_global_rhs(u_ls)
assert round((u_lu.vector() - u_ls.vector()).norm("l2"), 12) == 0
# Compute solution with local solver (Cholesky) and compare
local_solver = LocalSolver(a, L, LocalSolver.SolverType.Cholesky)
u_ls = Function(U)
local_solver.solve_global_rhs(u_ls)
assert round((u_lu.vector() - u_ls.vector()).norm("l2"), 12) == 0
def test_solve_local(ghost_mode):
mesh = UnitIntervalMesh(50)
U = FunctionSpace(mesh, "DG", 2)
# Set initial values
u0 = interpolate(Expression("cos(pi*x[0])", degree=2), U)
# Define test and trial functions
v, u = TestFunction(U), TrialFunction(U)
# Set time step size
dt = Constant(2.0e-4)
# Define fluxes on interior and exterior facets
u_hat = avg(u0) + 0.25*jump(u0)
u_hatbnd = -u0 + 0.25*(u0 - 1.0)
# Define variational formulation
a = u*v*dx
L = (u0*v + dt*u0*v.dx(0))*dx - dt*u_hat*jump(v)*dS - dt*u_hatbnd*v*ds
b = assemble(L)
# Compute reference solution with global LU solver
u_lu = Function(U)
solve(a == L, u_lu, solver_parameters = {"linear_solver" : "lu"})
# Compute solution with local solver and compare
local_solver = LocalSolver(a)
u_ls = Function(U)
local_solver.solve_local(u_ls.vector(), b, U.dofmap())
assert round((u_lu.vector() - u_ls.vector()).norm("l2"), 12) == 0
# Compute solution with local solver (Cholesky) and compare
local_solver = LocalSolver(a, solver_type=LocalSolver.SolverType.Cholesky)
u_ls = Function(U)
local_solver.solve_local(u_ls.vector(), b, U.dofmap())
assert round((u_lu.vector() - u_ls.vector()).norm("l2"), 12) == 0
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