def test_dy_dxi():
'''
This test checks the derivative :math:`\\frac{\\partial y}{\\partial \\xi}`
calculated using the function :math:`dg_maxwell.wave_equation_2d.dy_dxi`
for the :math:`0^{th}` element of a mesh for a circular ring. You may
download the file from this
:download:`link <../dg_maxwell/tests/wave_equation_2d/files/circle.msh>`.
'''
threshold = 1e-7
dy_dxi_reference = af.np_to_af_array(
utils.csv_to_numpy(
'dg_maxwell/tests/wave_equation_2d/files/dy_dxi_data.csv'))
nodes, elements = msh_parser.read_order_2_msh(
'dg_maxwell/tests/wave_equation_2d/files/circle.msh')
N_LGL = 16
xi_LGL = lagrange.LGL_points(N_LGL)
eta_LGL = lagrange.LGL_points(N_LGL)
Xi = af.data.tile(af.array.transpose(xi_LGL), d0=N_LGL)
Eta = af.data.tile(eta_LGL, d0=1, d1=N_LGL)
dy_dxi = wave_equation_2d.dy_dxi(nodes[elements[0]][:, 1], Xi, Eta)
check = af.abs(dy_dxi - dy_dxi_reference) < threshold
assert af.all_true(check)
def test_Li_basis_value():
'''
This test compares the output of the lagrange basis value calculated by the
function ``Li_basis_value`` to the analytical value of the lagrange
polynomials created using the same LGL points.
The analytical values were calculated in this sage worksheet_
.. _worksheet: https://goo.gl/ADyA3U
'''
threshold = 1e-11
Li_value_ref = af.np_to_af_array(utils.csv_to_numpy(
'dg_maxwell/tests/lagrange/files/Li_value.csv'))
N_LGL = 8
xi_LGL = lagrange.LGL_points(N_LGL)
L_basis_poly1d, L_basis_af = lagrange.lagrange_polynomials(xi_LGL)
L_basis_af = af.np_to_af_array(L_basis_af)
Li_indexes = af.np_to_af_array(np.arange(3, dtype = np.int32))
xi = af.np_to_af_array(np.linspace(-1., 1, 10))
Li_value = lagrange.Li_basis_value(L_basis_af, Li_indexes, xi)
assert af.all_true(af.abs(Li_value - Li_value_ref) < threshold)
def test_A_matrix():
'''
Compares the tensor product calculated using the ``A_matrix`` function
with an analytic value of the tensor product for :math:`N_{LGL} = 4`.
The analytic value of the tensor product is calculated in this
`document`_
.. _document: https://goo.gl/QNWxXp
'''
threshold = 1e-12
A_matrix_ref = af.np_to_af_array(
utils.csv_to_numpy(
'dg_maxwell/tests/wave_equation_2d/files/A_matrix_ref.csv'))
params.N_LGL = 4
advec_var = gvar.advection_variables(params.N_LGL, params.N_quad,
params.x_nodes, params.N_Elements,
params.c, params.total_time,
params.wave, params.c_x, params.c_y,
params.courant, params.mesh_file,
params.total_time_2d)
A_matrix_test = wave_equation_2d.A_matrix(params.N_LGL, advec_var)
assert af.max(af.abs(A_matrix_test - A_matrix_ref)) < threshold