def assemble_with_mixed_types(
mesh: Mesh,
diffusions: List[Coefficient],
convections: List[Optional[Coefficient]],
reactions: List[Optional[Coefficient]],
):
for diffusion in diffusions:
for convection in convections:
for reaction in reactions:
eafe_assemble(mesh, diffusion, convection, reaction)
def assert_solves(
mesh: Mesh,
diffusion: Coefficient,
convection: Optional[Coefficient],
reaction: Optional[Coefficient],
source: Coefficient,
exact: Coefficient,
l2_tol: Optional[float] = 1.0e-8,
h1_tol: Optional[float] = 1.0e-6,
):
eafe_matrix = eafe_assemble(mesh, diffusion, convection, reaction)
pw_linears = FunctionSpace(mesh, "Lagrange", 1)
test_function = TestFunction(pw_linears)
rhs_vector = assemble(source * test_function * dx)
bc = DirichletBC(pw_linears, exact, lambda _, on_bndry: on_bndry)
bc.apply(eafe_matrix, rhs_vector)
solution = Function(pw_linears)
solver = LUSolver(eafe_matrix, "default")
solver.parameters["symmetric"] = False
solver.solve(solution.vector(), rhs_vector)
l2_err: float = errornorm(exact, solution, "l2", 3)
assert l2_err <= l2_tol, f"L2 error too large: {l2_err} > {l2_tol}"
h1_err: float = errornorm(exact, solution, "H1", 3)
assert h1_err <= h1_tol, f"H1 error too large: {h1_err} > {h1_tol}"
def run():
def boundary(x, on_boundary):
return on_boundary
diffusivity = 1.0E-2
def diffusion_expression(x):
return diffusivity
def convection_expression(x):
return np.array([x[1], -x[0], 0.0])
exact_solution = Expression(
"sin(2 * DOLFIN_PI * x[0]) * cos(2 * DOLFIN_PI * x[1])", degree=4)
right_side_expression = Expression(
"8 * DOLFIN_PI * DOLFIN_PI * diffusivity\
* sin(2 * DOLFIN_PI * x[0]) * cos(2 * DOLFIN_PI * x[1])\
- 2 * DOLFIN_PI * x[1] * cos(2 * DOLFIN_PI * x[0])\
* cos(2 * DOLFIN_PI * x[1])\
- 2 * DOLFIN_PI * x[0] * sin(2 * DOLFIN_PI * x[0])\
* sin(2 * DOLFIN_PI * x[1])",
degree=2,
diffusivity=diffusivity)
granularity = 8
mesh = UnitCubeMesh(granularity, granularity, granularity)
continuous_pw_linear_space = FunctionSpace(mesh, "Lagrange", 1)
test_function = TestFunction(continuous_pw_linear_space)
linear_functional = right_side_expression * test_function * dx
stiffness_matrix = pyeafe.eafe_assemble(mesh, diffusion_expression,
convection_expression)
rhs_vector = assemble(linear_functional)
bc = DirichletBC(continuous_pw_linear_space, exact_solution, boundary)
bc.apply(stiffness_matrix, rhs_vector)
solution = Function(continuous_pw_linear_space)
solver = LUSolver(stiffness_matrix, "default")
solver.parameters["symmetric"] = False
solver.solve(solution.vector(), rhs_vector)
if (errornorm(exact_solution, solution, 'l2', 3) > 2.12E-1):
print "L2 error increased! Solver failed"
exit(1)
if (errornorm(exact_solution, solution, 'H1', 3) > 2.33E-0):
print "H1 error increased! Solver failed"
exit(1)
print "L2 error = ", errornorm(exact_solution, solution, 'l2', 3)
print "H1 error = ", errornorm(exact_solution, solution, 'H1', 3)
print "Success!"
def test_assemble_raises_for_invalid_convection():
with pytest.raises(TypeError):
eafe_assemble(MESH, DIFFUSION, 5.0)
with pytest.raises(ValueError):
eafe_assemble(MESH, DIFFUSION, Expression("1.", degree=1))
with pytest.raises(ValueError):
eafe_assemble(MESH, DIFFUSION, Expression(("1."), degree=1))
def run():
logging.getLogger('FFC').setLevel(logging.WARNING)
granularity = 8
mesh = UnitSquareMesh(granularity, granularity)
def diffusion(x):
return diffusivity
def convection(x):
return np.array([x[1], -x[0]])
eafe = pyeafe.eafe_assemble(mesh, diffusion, convection)
try:
compute_error(eafe, mesh)
except error:
print("error when executing with python defined coefficients")
print(error)
exit(1)
diffusion_expression = Expression("diffusivity",
diffusivity=diffusivity, degree=2)
convection_expression = Expression(("x[1]", "-x[0]"), degree=2)
eafe_expression = pyeafe.eafe_assemble(
mesh,
diffusion_expression,
convection_expression
)
try:
compute_error(eafe_expression, mesh)
except error:
print("error when executing with python defined coefficients")
print(error)
exit(1)
cg = FunctionSpace(mesh, "CG", 1)
bdm = FunctionSpace(mesh, "BDM", 1)
diffusion_interpolant = interpolate(diffusion_expression, cg)
convection_interpolant = interpolate(convection_expression, bdm)
eafe_function = pyeafe.eafe_assemble(
mesh,
diffusion_interpolant,
convection_interpolant
)
try:
compute_error(eafe_function, mesh)
except error:
print("error when executing with python defined coefficients")
print(error)
exit(1)
eafe_constant = pyeafe.eafe_assemble(mesh, diffusivity, np.zeros(2))
try:
diff_expr = Expression("diff", degree=2, diff=diffusivity)
zero_expr = Expression("zero", degree=2, zero=0.0)
err = compute_error(eafe_constant, mesh, diff_expr, zero_expr)
except error:
print("error when executing with constant coefficients")
print(error)
exit(1)
print "Errors for various PDE coefficient representations are acceptable"
print "Success!"
* sin(2 * DOLFIN_PI * x[0]) * cos(2 * DOLFIN_PI * x[1])\
- 2 * DOLFIN_PI * x[1] * cos(2 * DOLFIN_PI * x[0])\
* cos(2 * DOLFIN_PI * x[1])\
- 2 * DOLFIN_PI * x[0] * sin(2 * DOLFIN_PI * x[0])\
* sin(2 * DOLFIN_PI * x[1])",
degree=2,
diffusivity=diffusivity)
granularity = 8
mesh = UnitSquareMesh(granularity, granularity)
continuous_pw_linear_space = FunctionSpace(mesh, "Lagrange", 1)
test_function = TestFunction(continuous_pw_linear_space)
linear_functional = right_side_expression * test_function * dx
stiffness_matrix = pyeafe.eafe_assemble(mesh, diffusion_expression,
convection_expression)
rhs_vector = assemble(linear_functional)
exact_solution = Expression(
"sin(2 * DOLFIN_PI * x[0]) * cos(2 * DOLFIN_PI * x[1])", degree=4)
bc = DirichletBC(continuous_pw_linear_space, exact_solution, boundary)
bc.apply(stiffness_matrix, rhs_vector)
solution = Function(continuous_pw_linear_space)
solver = LUSolver(stiffness_matrix, "default")
solver.parameters["symmetric"] = False
solver.solve(solution.vector(), rhs_vector)
if (errornorm(exact_solution, solution, 'l2', 3) > 2.12E-1):
print "L2 error increased! Solver failed"
exit(1)
def test_assemble_raises_for_invalid_reaction():
with pytest.raises(TypeError):
eafe_assemble(MESH, DIFFUSION, CONVECTION, 5.0)
with pytest.raises(TypeError):
eafe_assemble(MESH, DIFFUSION, reaction=5.0)
def test_assemble_raises_for_invalid_diffusion():
with pytest.raises(TypeError):
eafe_assemble(MESH, None)
with pytest.raises(TypeError):
eafe_assemble(MESH, 1.0)
def test_assemble_raises_for_invalid_mesh():
with pytest.raises(TypeError):
eafe_assemble(None, DIFFUSION)