def test_functional3D():
"""Test integration of function interpolated in non-matching meshes"""
f = Quadratic3D()
# Interpolate quadratic function on course mesh
mesh0 = UnitCubeMesh(8, 8, 8)
V0 = FunctionSpace(mesh0, "Lagrange", 2)
u0 = interpolate_nonmatching_mesh(f, V0)
# Interpolate FE function on finer mesh
mesh1 = UnitCubeMesh(21, 21, 21)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = interpolate_nonmatching_mesh(u0, V1)
assert round(assemble(u0*dx) - assemble(u1*dx), 10) == 0
mesh1 = UnitCubeMesh(20, 20, 20)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = interpolate_nonmatching_mesh(u0, V1)
assert round(assemble(u0*dx) - assemble(u1*dx), 10) == 0
f = Expression(("x[0]*x[0] + x[1]*x[1]",
"x[0]*x[0] + x[1]*x[1] + 1",
"x[0]*x[0] + x[1]*x[1] + 2"))
V0 = FunctionSpace(mesh0, "Nedelec 1st kind H(curl)", 2)
u0 = interpolate(f, V0)
# Interpolate FE function on finer mesh
V1 = FunctionSpace(mesh1, "Nedelec 1st kind H(curl)", 2)
u1 = interpolate_nonmatching_mesh_any(u0, V1)
assert round(assemble(dot(u0, u0)*dx) - assemble(dot(u1, u1)*dx), 2) == 0
def test_functional3D():
"""Test integration of function interpolated in non-matching meshes"""
f = Quadratic3D(degree=2)
# Interpolate quadratic function on course mesh
mesh0 = UnitCubeMesh(8, 8, 8)
V0 = FunctionSpace(mesh0, "Lagrange", 2)
u0 = interpolate_nonmatching_mesh(f, V0)
# Interpolate FE function on finer mesh
mesh1 = UnitCubeMesh(21, 21, 21)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = interpolate_nonmatching_mesh(u0, V1)
assert round(assemble(u0 * dx) - assemble(u1 * dx), 10) == 0
mesh1 = UnitCubeMesh(20, 20, 20)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = interpolate_nonmatching_mesh(u0, V1)
assert round(assemble(u0 * dx) - assemble(u1 * dx), 10) == 0
f = Expression(("x[0]*x[0] + x[1]*x[1]", "x[0]*x[0] + x[1]*x[1] + 1",
"x[0]*x[0] + x[1]*x[1] + 2"),
degree=2)
V0 = FunctionSpace(mesh0, "Nedelec 1st kind H(curl)", 2)
u0 = interpolate(f, V0)
# Interpolate FE function on finer mesh
V1 = FunctionSpace(mesh1, "Nedelec 1st kind H(curl)", 2)
u1 = interpolate_nonmatching_mesh_any(u0, V1)
assert round(assemble(dot(u0, u0) * dx) - assemble(dot(u1, u1) * dx),
2) == 0
def test_functional2D():
"""Test integration of function interpolated in non-matching meshes"""
f = Quadratic2D(degree=2)
# Interpolate quadratic function on course mesh
mesh0 = UnitSquareMesh(8, 8)
V0 = FunctionSpace(mesh0, "Lagrange", 2)
u0 = interpolate_nonmatching_mesh(f, V0)
# Interpolate FE function on finer mesh
mesh1 = UnitSquareMesh(31, 31)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = interpolate_nonmatching_mesh(u0, V1)
assert round(assemble(u0*dx) - assemble(u1*dx), 10) == 0
mesh1 = UnitSquareMesh(30, 30)
V1 = FunctionSpace(mesh1, "Lagrange", 2)
u1 = interpolate_nonmatching_mesh(u0, V1)
assert round(assemble(u0*dx) - assemble(u1*dx), 10) == 0
f = Expression(("x[0]*x[0] + x[1]*x[1]",
"x[0]*x[0] + x[1]*x[1] + 1"), degree=2)
V0 = FunctionSpace(mesh0, "Nedelec 1st kind H(curl)", 2)
u0 = interpolate(f, V0)
# Interpolate FE function on finer mesh
V1 = FunctionSpace(mesh1, "Nedelec 1st kind H(curl)", 2)
u1 = interpolate_nonmatching_mesh_any(u0, V1)
assert round(assemble(dot(u0, u0)*dx) - assemble(dot(u1, u1)*dx), 4) == 0
# Test with another expression
f = Expression(("2*(x[0]*x[0] + x[1]*x[1])",
"2*(x[0]*x[0] + x[1]*x[1] + 1)"), degree=2)
u0 = interpolate_nonmatching_mesh_any(f, V0)
u1 = interpolate_nonmatching_mesh_any(u0, V1)
assert round(assemble(dot(u0, u0)*dx) - assemble(dot(u1, u1)*dx), 4) == 0