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"""Unit tests for interpolation using LagrangeInterpolator"""
# Copyright (C) 2014 Mikael Mortensen
#
# 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/>.
#
# First added: 2014-02-18
# Last changed:
import unittest
import numpy
from dolfin import *
class Quadratic2D(Expression):
def eval(self, values, x):
values[0] = x[0]*x[0] + x[1]*x[1] + 1.0
class Quadratic3D(Expression):
def eval(self, values, x):
values[0] = x[0]*x[0] + x[1]*x[1] + x[2]*x[2] + 1.0
class LagrangeInterpolatorTest(unittest.TestCase):
def test_functional2D(self):
"""Test integration of function interpolated in non-matching meshes"""
f = Quadratic2D()
ll = LagrangeInterpolator()
# Interpolate quadratic function on course mesh
mesh0 = UnitSquareMesh(8, 8)
V0 = FunctionSpace(mesh0, "Lagrange", 2)
u0 = Function(V0)
ll.interpolate(u0, f)
# Interpolate FE function on finer mesh
mesh1 = UnitSquareMesh(31, 31)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = Function(V1)
ll.interpolate(u1, u0)
self.assertAlmostEqual(assemble(u0*dx), assemble(u1*dx), 10)
mesh1 = UnitSquareMesh(30, 30)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = Function(V1)
ll.interpolate(u1, u0)
self.assertAlmostEqual(assemble(u0*dx), assemble(u1*dx), 10)
def test_functional3D(self):
"""Test integration of function interpolated in non-matching meshes"""
f = Quadratic3D()
ll = LagrangeInterpolator()
# Interpolate quadratic function on course mesh
mesh0 = UnitCubeMesh(4, 4, 4)
V0 = FunctionSpace(mesh0, "Lagrange", 2)
u0 = Function(V0)
ll.interpolate(u0, f)
# Interpolate FE function on finer mesh
mesh1 = UnitCubeMesh(11, 11, 11)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = Function(V1)
ll.interpolate(u1, u0)
self.assertAlmostEqual(assemble(u0*dx), assemble(u1*dx), 10)
mesh1 = UnitCubeMesh(10, 11, 10)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = Function(V1)
ll.interpolate(u1, u0)
self.assertAlmostEqual(assemble(u0*dx), assemble(u1*dx), 10)
if __name__ == "__main__":
unittest.main()
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