def test_collocation_points_chebyshev_gauss(self):
for num_coll_points in range(2, 13):
coefs = np.zeros(num_coll_points + 1)
coefs[-1] = 1.
coll_points_numpy = chebyshev.chebroots(coefs)
mesh = Mesh1D(num_coll_points, Basis.Chebyshev, Quadrature.Gauss)
coll_points_spectre = collocation_points(mesh)
np.testing.assert_allclose(coll_points_numpy, coll_points_spectre,
1e-12, 1e-12)
def test_collocation_points_chebyshev_gauss_lobatto(self):
for num_coll_points in range(2, 13):
coefs = np.zeros(num_coll_points)
coefs[-1] = 1.
coll_points_numpy = np.concatenate(
([-1.], chebyshev.Chebyshev(coefs).deriv().roots(), [1.]))
mesh = Mesh1D(num_coll_points, Basis.Chebyshev,
Quadrature.GaussLobatto)
coll_points_spectre = collocation_points(mesh)
np.testing.assert_allclose(coll_points_numpy, coll_points_spectre,
1e-12, 1e-12)
def test_modal_to_nodal_matrix_chebyshev(self):
for quadrature in [Quadrature.Gauss, Quadrature.GaussLobatto]:
for num_coll_points in range(2, 13):
mesh = Mesh1D(num_coll_points, Basis.Chebyshev, quadrature)
coll_points = collocation_points(mesh)
mtn_numpy = chebyshev.chebvander(coll_points,
num_coll_points - 1)
mtn_spectre = modal_to_nodal_matrix(mesh)
np.testing.assert_allclose(mtn_spectre, mtn_numpy, 1e-12,
1e-12)
ntm_spectre = nodal_to_modal_matrix(mesh)
np.testing.assert_allclose(np.matmul(mtn_spectre, ntm_spectre),
np.identity(num_coll_points), 1e-12,
1e-12)