def test_traction_mirror_symmety():
kernel = TractionKernel(1.0, 0.25)
a = np.array(kernel.call(np.array([1.0, 0.5]),
np.zeros(2), np.array([1.0, 0.0])))
# Only symmetric if we reverse the normal vector too!
b = np.array(kernel.call(np.array([-1.0, -0.5]),
np.zeros(2), np.array([-1.0, 0.0])))
np.testing.assert_almost_equal(a, b)
def test_traction():
kernel = TractionKernel(1.0, 0.25)
H = kernel.call(np.array([2.0, 0.0]),
np.array([0, 0.0]),
np.array([0, 1.0]))
np.testing.assert_almost_equal(H[0][1],
1 / (6 * np.pi * 2.0))
np.testing.assert_almost_equal(H[0][0], 0.0)
np.testing.assert_almost_equal(H[1][1], 0.0)
np.testing.assert_almost_equal(H[1][0], -H[0][1])
def test_traction_kernel_elements():
E = 1e5
nu = 0.3
shear_modulus = E / (2 * (1 + nu))
kernel = TractionKernel(shear_modulus, nu)
T = kernel.call(np.array([0, 4.7285]),
np.zeros(2),
np.array([-1.0, 0.0]))
exact = np.array([[0, 0.0096],[-0.0096, 0]])
np.testing.assert_almost_equal(exact, np.array(T), 4)
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 test_fast_lobatto():
N = 15
mesh = simple_line_mesh(1, (0, 0), (1, 0))
mapping = PolynomialMapping(mesh.elements[0])
kernel = TractionKernel(1.0, 0.25)
bf = gll_basis(N)
one = ConstantBasis(np.ones(2))
quad_info_old = lobatto(N + 1)
pt = [0.0, -5.0]
normal = [0.0, 1.0]
kernel.set_interior_data(pt, normal)
est_slow = single_integral(mapping.eval, kernel, one, bf, quad_info_old, 0, 0)
est_fast = aligned_single_integral(mapping.eval, kernel, bf, quad_info_old, 0)
np.testing.assert_almost_equal(np.array(est_slow), np.array(est_fast))
def test_gauss_displacement_xy():
mesh = simple_line_mesh(1, (0, 0), (1, 0))
mapping = PolynomialMapping(mesh.elements[0])
kernel = TractionKernel(1.0, 0.25)
degree = 4
bf = gll_basis(degree)
one = ConstantBasis(np.ones(2))
quad_info_exact = gauss(100)
quad_info = lobatto(degree + 1)
# Testing GLL basis and quadrature combination on the nonsingular part
# of the displacement kernel.
pt = [0.5, 1000.0]
normal = [0.0, 1.0]
kernel.set_interior_data(pt, normal)
integrate = lambda qi: single_integral(mapping.eval, kernel, one, bf, qi, 0, 0)
exact = integrate(quad_info_exact)
est = integrate(quad_info)
np.testing.assert_almost_equal(exact[0][1], est[0][1], 16)
def test_rl_integral():
mesh = simple_line_mesh(1, (0, 0), (1, 0))
mapping = PolynomialMapping(mesh.elements[0])
kernel = TractionKernel(1.0, 0.25)
bf = gll_basis(4)
one = ConstantBasis(np.ones(2))
quad_info_old = lobatto(5)
x_bf = np.array(bf.nodes)
x_q = np.array(quad_info_old.x)
distance = 5.0
quad_info_new = rl_quad(5, 0.0, distance)
# This one is comparing lobatto quadrature and recursive legendre quadrature
# on the TractionKernel which is 1/r singular.
pt = [0.0, -distance]
normal = [0.0, 1.0]
# exact = 0.2473475767
exact = 0.00053055607635
integrate = lambda qi: single_integral(mapping.eval, kernel, one, bf, qi, 0, 0)
aligned_integrate = lambda qi: aligned_single_integral(mapping.eval, kernel, bf, qi, 0)
kernel.set_interior_data(pt, normal)
est_gauss = integrate(quad_info_old)
np.testing.assert_almost_equal(est_gauss[0][0], exact)
est_gauss_fast = aligned_integrate(quad_info_old)
np.testing.assert_almost_equal(est_gauss_fast[0][0], exact)
# This stuff doesn't work yet
est_new = integrate(quad_info_new)
np.testing.assert_almost_equal(est_new[0][0], exact, 6)
est_new_fast = aligned_integrate(quad_info_new)
np.testing.assert_almost_equal(est_new_fast[0][0], exact, 6)
