def test_degree_zero_eval():
bf = basis_from_degree(0)
assert(bf.n_fncs == 1)
for x in np.linspace(0.0, 1.0, 10):
my_assert(bf.evaluate(0, x), 1.0)
deriv = bf.get_gradient_basis().evaluate(0, x)
my_assert(deriv, 0.0)
def simple_mass_matrix(n_elements = 2, continuous = False):
bf = basis_funcs.basis_from_degree(1)
msh = simple_line_mesh(n_elements)
q = quadrature.gauss(2)
apply_to_elements(msh, "basis", bf, non_gen = True)
apply_to_elements(msh, "continuous", continuous, non_gen = True)
init_dofs(msh)
return assemble_mass_matrix(msh, q)
def test_M_integral_same_dof_with_jacobian():
msh = simple_line_mesh(4)
q = quadrature.gauss(2)
bf = basis_funcs.basis_from_degree(1)
kernel = MassMatrixKernel(0, 0)
M_local = single_integral(msh.elements[0].mapping.eval, kernel, bf,
bf, q, 0, 0)
# Element size divided by two so the M value should be divided by two
np.testing.assert_almost_equal(M_local[0][0], 1.0 / 6.0)
def test_M_integral_diff_dof():
msh = simple_line_mesh(2)
q = quadrature.gauss(2)
bf = basis_funcs.basis_from_degree(1)
kernel = MassMatrixKernel(0, 0)
M_local = single_integral(msh.elements[0].mapping.eval, kernel, bf,
bf, q, 0, 1)
# integral of (1-x)*x from 0 to 1
np.testing.assert_almost_equal(M_local[0][0], 1.0 / 6.0)
def test_basis_from_func():
msh = simple_line_mesh(1)
bf = basis_from_degree(1)
soln = basis_from_func(bf, lambda x, n: x, msh.elements[0])
value = soln.evaluate(0, 0.0)
np.testing.assert_almost_equal(value, [-1.0, 0.0])
value = soln.evaluate(1, 1.0)
np.testing.assert_almost_equal(value, [1.0, 0.0])
def test_solution():
msh = simple_line_mesh(1)
bf = basis_from_degree(1)
soln = CoeffBasis(bf, np.array([[0.0, 1.0], [1.0, 0.0]]))
value = soln.evaluate(0, 0.0)
np.testing.assert_almost_equal(value, [0.0, 1.0])
value = soln.evaluate(1, 1.0)
np.testing.assert_almost_equal(value, [1.0, 0.0])
def test_apply_solution():
msh = simple_line_mesh(2)
solution_coeffs = np.array([0.0, 1.0, 2.0, 3.0])
bf = basis_from_degree(0)
apply_to_elements(msh, "basis", bf, non_gen = True)
apply_to_elements(msh, "continuous", False, non_gen = True)
init_dofs(msh)
apply_coeffs(msh, solution_coeffs, "soln")
np.testing.assert_almost_equal(
msh.elements[1].soln.evaluate(0, 1.), [1.0, 3.0])
def test_plot_single_integral_kernel():
msh = simple_line_mesh(2)
x = np.linspace(0.0, 1, 1000)
kernel = TractionKernel(1.0, 0.25)
bf = basis_funcs.basis_from_degree(8)
bf1 = ConstantBasis((1.0, 1.0))
k = np.zeros_like(x)
k_int = np.zeros_like(x)
for (i, x_val) in enumerate(x):
q = quadrature.piessens(16, x_val, 16)
kernel.set_interior_data([x_val, 0.0], [0.0,1.0])
kd = kernel.get_interior_integral_data([1.0, 0.0], [0.0, 1.0])
k[i] = kernel._call(kd, 0, 1)
k_int[i] = single_integral(msh.elements[1].mapping.eval, kernel, bf1,
bf, q, 0, 4)[0][1]
def simple_assembler(degree = 0,
nonsing_pts = 2,
logr_pts = 2,
oneoverr_pts = 2,
n_elements = 2):
if oneoverr_pts % 2 == 1:
oneoverr_pts += 1
msh = simple_line_mesh(n_elements)
qs = quad_strategy.QuadStrategy(msh, nonsing_pts, nonsing_pts,
logr_pts, oneoverr_pts)
bf = basis_funcs.basis_from_degree(degree)
apply_to_elements(msh, "basis", bf, non_gen = True)
apply_to_elements(msh, "continuous", False, non_gen = True)
apply_to_elements(msh, "qs", qs, non_gen = True)
init_dofs(msh)
return msh
def test_realistic_double_integral_symmetry():
msh = simple_line_mesh(2)
bf = basis_funcs.basis_from_degree(1)
qs = quad_strategy.QuadStrategy(msh, 10, 10, 10, 10)
kernel = DisplacementKernel(1.0, 0.25)
# fnc = lambda r, n: 1 / r[0]
one = double_integral(msh.elements[1].mapping.eval, msh.elements[1].mapping.eval, kernel, bf,
bf, qs.get_simple(),
qs.quad_logr, 0, 1)
two = double_integral(msh.elements[1].mapping.eval, msh.elements[1].mapping.eval, kernel, bf,
bf, qs.get_simple(),
qs.quad_logr, 1, 0)
one = np.array(one)
two = np.array(two)
np.testing.assert_almost_equal(one, two)
def realistic_assembler(n_elements = 4,
element_deg = 1,
quad_points_nonsingular = 5,
quad_points_logr = 6,
quad_points_oneoverr = 5,
left = -1.0,
right = 1.0):
dim = 2
if quad_points_oneoverr % 2 == 1:
quad_points_oneoverr += 1
msh = simple_line_mesh(n_elements, (left, 0.0), (right, 0.0))
bf = basis_funcs.basis_from_degree(element_deg)
qs = quad_strategy.QuadStrategy(msh, quad_points_nonsingular,
quad_points_nonsingular,
quad_points_logr, quad_points_oneoverr)
apply_to_elements(msh, "basis", bf, non_gen = True)
apply_to_elements(msh, "continuous", True, non_gen = True)
apply_to_elements(msh, "qs", qs, non_gen = True)
init_dofs(msh)
return msh
def test_exact_dbl_integrals_H_same_element():
msh = simple_line_mesh(1)
qs = quad_strategy.QuadStrategy(msh, 10, 10, 10, 10)
qo = qs.get_simple()
qi = qs.quad_oneoverr
bf = basis_funcs.basis_from_degree(1)
kernel = TractionKernel(1.0, 0.25)
H_00 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval,
kernel,
bf, bf, qo,
qi, 0, 0)
np.testing.assert_almost_equal(H_00, np.zeros((2, 2)), 3)
H_11 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval,
kernel,
bf, bf, qo,
qi, 1, 1)
np.testing.assert_almost_equal(H_11, np.zeros((2, 2)), 3)
H_01 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval,
kernel, bf,
bf, qo,
qi, 0, 1)
H_01_exact = np.array([[0.0, 1 / (6 * np.pi)],
[-1 / (6 * np.pi), 0.0]])
np.testing.assert_almost_equal(H_01, H_01_exact, 3)
H_10 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval,
kernel, bf,
bf, qo,
qi, 1, 0)
H_10_exact = np.array([[0.0, -1 / (6 * np.pi)],
[1 / (6 * np.pi), 0.0]])
np.testing.assert_almost_equal(H_10, H_10_exact, 3)
def test_exact_dbl_integrals_G_different_element():
msh = simple_line_mesh(2)
bf = basis_funcs.basis_from_degree(1)
qs = quad_strategy.QuadStrategy(msh, 10, 10, 10, 10)
qo = qs.get_simple()
qi = qs.quad_logr
kernel = DisplacementKernel(1.0, 0.25)
G_00 = double_integral(msh.elements[0].mapping.eval, msh.elements[1].mapping.eval, kernel, bf,
bf, qo, qi, 0, 0)
G_10 = double_integral(msh.elements[0].mapping.eval, msh.elements[1].mapping.eval, kernel, bf,
bf, qo, qi, 1, 0)
G_01 = double_integral(msh.elements[0].mapping.eval, msh.elements[1].mapping.eval, kernel, bf,
bf, qo, qi, 0, 1)
G_11 = double_integral(msh.elements[0].mapping.eval, msh.elements[1].mapping.eval, kernel, bf,
bf, qo, qi, 1, 1)
np.testing.assert_almost_equal(G_10,
[[0.02833119, 0], [0, 0.01506828]], 4)
np.testing.assert_almost_equal(G_01,
[[0.00663146, 0], [0, -0.00663146]], 4)
np.testing.assert_almost_equal(G_00, [[0.0150739, 0], [0, 0.00181103]], 4)
np.testing.assert_almost_equal(G_11, [[0.0150739, 0], [0, 0.00181103]], 4)
def test_exact_dbl_integrals_G_same_element():
msh = simple_line_mesh(1)
bf = basis_funcs.basis_from_degree(1)
qs = quad_strategy.QuadStrategy(msh, 10, 10, 10, 10)
qo = qs.get_simple()
qi = qs.quad_logr
kernel = DisplacementKernel(1.0, 0.25)
G_00 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval, kernel, bf,
bf, qo, qi, 0, 0)
np.testing.assert_almost_equal(G_00, [[0.165187, 0], [0, 0.112136]], 4)
G_10 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval, kernel, bf,
bf, qo, qi, 1, 0)
np.testing.assert_almost_equal(G_10, [[0.112136, 0], [0, 0.0590839]], 4)
G_01 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval, kernel, bf,
bf, qo, qi, 0, 1)
np.testing.assert_almost_equal(G_01, [[0.112136, 0], [0, 0.0590839]], 4)
G_11 = double_integral(msh.elements[0].mapping.eval,
msh.elements[0].mapping.eval, kernel, bf,
bf, qo, qi, 1, 1)
np.testing.assert_almost_equal(G_11, [[0.165187, 0], [0, 0.112136]], 4)
def test_poly_basis_derivs():
bf = basis_from_degree(1)
my_assert(bf.point_sources, [[0.0, 1.0, 1.0], [1.0, 1.0, 1.0]])
my_assert(bf.point_source_dependency, [0, 1])
def test_grad_basis_derivs():
bf = basis_from_degree(1).get_gradient_basis()
my_assert(bf.point_sources, [])
def test_coeff_basis_derivs():
bf = CoeffBasis(basis_from_degree(1), [[0.0, 1.0], [1.0, 0.0]])
my_assert(bf.point_sources, [[0.0, 1.0, 1.0], [1.0, 1.0, 1.0]])
my_assert(bf.point_source_dependency, [0, 1])