def test_weighted_metric(self):
# TODO: figure out why if the metric tensor is set to ones the result is very different
"""Compare weighted and unweighted metric terms with K set to identity."""
mesh = CrazyMesh(2, (1, 1), ((-1, 1), (-1, 1)), curvature=0.2)
K = MeshFunction(mesh)
func_space = FunctionSpace(mesh, '1-lobatto', (3, 3))
basis = BasisForm(func_space)
K.continous_tensor = [diff_tens_11, diff_tens_12, diff_tens_22]
xi = eta = np.linspace(-1, 1, 5)
xi, eta = np.meshgrid(xi, eta)
g_11_k, g_12_k, g_22_k = basis.weighted_metric_tensor(xi.ravel('F'), eta.ravel('F'), K)
g_11, g_12, g_22 = mesh.metric_tensor(xi.ravel('F'), eta.ravel('F'))
npt.assert_array_almost_equal(g_11, g_11_k)
def test_discretize_lobatto(self):
"""Test the discretize method of the 2 - forms."""
my_mesh = CrazyMesh(2, (2, 2), ((-1, 1), (-1, 1)), curvature=0)
p_int_0 = 2
for p in range(3, 8):
filename = 'discrete_2_form_p' + \
str(p) + '_p_int' + str(p_int_0) + '.dat'
directory = os.getcwd() + '/src/tests/test_discrete_2_form/'
func_space = FunctionSpace(my_mesh, '2-lobatto', p)
form = Form(func_space)
form.discretize(paraboloid, ('gauss', p_int_0))
cochain_ref = np.loadtxt(directory + filename, delimiter=',')
npt.assert_array_almost_equal(form.cochain_local,
cochain_ref,
decimal=4)
p = 5
for p_int in range(2, 6):
filename = 'discrete_2_form_p' + \
str(p) + '_p_int' + str(p_int_0) + '.dat'
directory = os.getcwd() + '/src/tests/test_discrete_2_form/'
func_space = FunctionSpace(my_mesh, '2-lobatto', p)
form = Form(func_space)
form.discretize(paraboloid, ('gauss', p_int_0))
cochain_ref = np.loadtxt(directory + filename, delimiter=',')
npt.assert_array_almost_equal(form.cochain_local,
cochain_ref,
decimal=4)
p = 6
p_int = 5
filename_1 = 'discrete_2_form_p' + \
str(p) + '_p_int' + str(p_int) + '_el_57.dat'
directory = os.getcwd() + '/src/tests/test_discrete_2_form/'
mesh_1 = CrazyMesh(2, (5, 7), ((-1, 1), (-1, 1)), curvature=0)
func_space = FunctionSpace(mesh_1, '2-lobatto', p)
form = Form(func_space)
form.discretize(paraboloid, ('gauss', p_int))
cochain_ref_1 = np.loadtxt(directory + filename_1, delimiter=',')
npt.assert_array_almost_equal(form.cochain_local, cochain_ref_1)
mesh_2 = CrazyMesh(2, (5, 7), ((-1, 1), (-1, 1)), curvature=0.2)
filename_2 = 'discrete_2_form_p' + \
str(p) + '_p_int' + str(p_int) + '_el_57_cc2.dat'
directory = os.getcwd() + '/src/tests/test_discrete_2_form/'
func_space = FunctionSpace(mesh_2, '2-lobatto', p)
form = Form(func_space)
form.discretize(paraboloid, ('gauss', p_int))
cochain_ref_2 = np.loadtxt(directory + filename_2, delimiter=',')
npt.assert_array_almost_equal(form.cochain_local, cochain_ref_2)
def test_visulalization_extended_gauss_e10_inner(self):
def pfun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (10, 10)
n = (20, 20)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
func_space_extGau = FunctionSpace(mesh, '0-ext_gauss', p)
form_0_extG = Form(func_space_extGau)
form_0_extG.discretize(self.pfun)
xi = eta = np.linspace(-1, 1, 10)
form_0_extG.reconstruct(xi, eta)
(x, y), data = form_0_extG.export_to_plot()
plt.contourf(x, y, data)
plt.title('reduced extended_gauss 0-form')
plt.colorbar()
plt.show()
form_1 = d(form_0_extG)
form_1.reconstruct(xi, eta)
(x, y), data_dx, data_dy = form_1.export_to_plot()
ufun_x, ufun_y = self.ufun()
plt.contourf(x, y, data_dx)
plt.title('extended_gauss 1-form dx')
plt.colorbar()
plt.show()
#
plt.contourf(x, y, data_dy)
plt.title('extended_gauss 1-form dy')
plt.colorbar()
plt.show()
print(np.min(data_dy))
def multiple_element():
mesh = CrazyMesh(2, (5, 7), ((-1, 1), (-1, 1)), curvature=0.3)
p = 10, 10
func_space_vort = FunctionSpace(mesh, '0-ext_gauss', (p[0] - 1, p[1] - 1), is_inner=False)
func_space_outer_vel = FunctionSpace(
mesh, '1-total_ext_gauss', (p[0], p[1]), is_inner=False)
# func_space_outer_vel = FunctionSpace(
# mesh, '1-gauss', (p[0], p[1]), is_inner=False)
func_space_inner_vel = FunctionSpace(mesh, '1-lobatto', p, is_inner=True)
func_space_inner_vel.dof_map.continous_dof = True
func_space_source = FunctionSpace(mesh, '2-lobatto', p, is_inner=True)
basis_vort = BasisForm(func_space_vort)
basis_vel_in = BasisForm(func_space_inner_vel)
basis_vel_in.quad_grid = 'lobatto'
basis_vel_out = BasisForm(func_space_outer_vel)
basis_vel_out.quad_grid = 'lobatto'
basis_2 = BasisForm(func_space_source)
psi = Form(func_space_vort)
u_in = Form(func_space_inner_vel)
source = Form(func_space_source)
source.discretize(ffun)
M_1 = inner(basis_vel_in, basis_vel_in)
E_21_in = d(func_space_inner_vel)
W_02 = basis_2.wedged(basis_vort)
W_02_E21 = np.transpose(W_02 @ E_21_in)
M_1 = assemble(M_1, (func_space_inner_vel, func_space_inner_vel))
print(np.shape(M_1))
W_02_E21 = assemble(W_02_E21, (func_space_inner_vel, func_space_vort))
print(np.shape(W_02_E21))
W_02 = assemble(W_02, (func_space_source, func_space_vort))
lhs = spr.bmat([[M_1, W_02_E21], [W_02_E21.transpose(), None]])
print(np.shape(lhs))
rhs = np.zeros(np.shape(lhs)[0])
rhs[-func_space_source.num_dof:] = W_02 @ source.cochain
solution = spr.linalg.spsolve(lhs.tocsc(), rhs)
u_in.cochain = solution[:func_space_inner_vel.num_dof]
cochian_psi = np.zeros(func_space_vort.num_dof)
cochian_psi[:func_space_vort.num_internal_dof] = solution[-func_space_vort.num_internal_dof:]
psi.cochain = cochian_psi
xi = eta = np.linspace(-1, 1, 40)
u_in.reconstruct(xi, eta)
(x, y), u_x, u_y = u_in.export_to_plot()
plt.contourf(x, y, u_x)
plt.colorbar()
plt.title("u_x inner")
plt.show()
psi.reconstruct(xi, eta)
(x, y), psi_value = psi.export_to_plot()
plt.contourf(x, y, psi_value)
plt.title("psi outer"
)
plt.colorbar()
plt.show()
def test_visulization_lobato_e10_inner(self):
def pfun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (20, 20)
n = (2, 2)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.2)
xi = eta = np.linspace(-1, 1, 100)
func_space = FunctionSpace(mesh, '0-lobatto', p)
form_0 = Form(func_space)
form_0.discretize(pfun)
form_0.reconstruct(xi, eta)
(x, y), data = form_0.export_to_plot()
plt.contourf(x, y, data)
plt.title('reduced lobatto 0-form')
plt.colorbar()
plt.show()
form_1 = d(form_0)
form_1.reconstruct(xi, eta)
(x, y), data_dx, data_dy = form_1.export_to_plot()
plt.contourf(x, y, data_dx)
plt.title('lobatto 1-form dx')
plt.colorbar()
# plt.show()
plt.contourf(x, y, data_dy)
plt.title('lobatto 1-form dy')
plt.colorbar()
# plt.show()
print(np.min(data_dy))
def test_inner(self):
list_cases = [
'p2_n2-2', 'p2_n3-2', 'p5_n1-10', 'p10_n2-2', 'p18_n14-14'
]
p = [2, 2, 5, 10, 18]
n = [(2, 2), (3, 2), (1, 10), (2, 2), (14, 10)]
curvature = [0.2, 0.1, 0.2, 0.2, 0.2]
for i, case in enumerate(list_cases[:-1]):
print("Test case n : ", i)
# basis = basis_forms.
# print("theo size ", (p[i] + 1)**2 *
# (p[i] + 1)**2 * n[i][0] * n[i][1])
M_0_ref = np.loadtxt(
os.getcwd() + '/src/tests/test_M_0/M_0_' + case + '.dat',
delimiter=',').reshape((p[i] + 1)**2, n[i][0] * n[i][1],
(p[i] + 1)**2)
# print(np.shape(M_0_ref))
my_mesh = CrazyMesh(2,
n[i], ((-1, 1), (-1, 1)),
curvature=curvature[i])
function_space = FunctionSpace(my_mesh, '0-lobatto', p[i])
basis = BasisForm(function_space)
basis.quad_grid = 'lobatto'
basis_1 = BasisForm(function_space)
basis_1.quad_grid = 'lobatto'
M_0 = inner(basis, basis_1)
for el in range(n[i][0] * n[i][1]):
npt.assert_array_almost_equal(M_0_ref[:, el, :],
M_0[:, :, el],
decimal=4)
def test_project_lobatto(self):
directory = 'src/tests/test_form_2/'
x_ref = np.loadtxt(directory + 'x_lobatto_n3-2_p20-20_c3_xieta_30.dat',
delimiter=',')
y_ref = np.loadtxt(directory + 'y_lobatto_n3-2_p20-20_c3_xieta_30.dat',
delimiter=',')
data_ref = np.loadtxt(directory +
'data_lobatto_n3-2_p20-20_c3_xieta_30.dat',
delimiter=',')
def ffun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (20, 20)
n = (3, 2)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
xi = eta = np.linspace(-1, 1, 30)
func_space = FunctionSpace(mesh, '2-lobatto', p)
form_2 = Form(func_space)
form_2.discretize(ffun)
form_2.reconstruct(xi, eta)
(x, y), data = form_2.export_to_plot()
npt.assert_array_almost_equal(x_ref, x)
npt.assert_array_almost_equal(y_ref, y)
npt.assert_array_almost_equal(data_ref, data)
def test_multiple_elements(self):
"""Test the anysotropic case in multiple element."""
p = (6, 6)
is_inner = False
crazy_mesh = CrazyMesh(2, (8, 5), ((-1, 1), (-1, 1)), curvature=0.1)
func_space_2_lobatto = FunctionSpace(crazy_mesh, '2-lobatto', p, is_inner)
func_space_1_lobatto = FunctionSpace(crazy_mesh, '1-lobatto', p, is_inner)
func_space_1_lobatto.dof_map.continous_dof = True
def diffusion_11(x, y): return 4 * np.ones(np.shape(x))
def diffusion_12(x, y): return 3 * np.ones(np.shape(x))
def diffusion_22(x, y): return 5 * np.ones(np.shape(x))
def source(x, y):
return -36 * np.pi ** 2 * np.sin(2 * np.pi * x) * np.sin(2 * np.pi * y) + 24 * np.pi ** 2 * np.cos(2 * np.pi * x) * np.cos(2 * np.pi * y)
# mesh function to inject the anisotropic tensor
mesh_k = MeshFunction(crazy_mesh)
mesh_k.continous_tensor = [diffusion_11, diffusion_12, diffusion_22]
# definition of the basis functions
basis_1 = BasisForm(func_space_1_lobatto)
basis_1.quad_grid = 'gauss'
basis_2 = BasisForm(func_space_2_lobatto)
basis_2.quad_grid = 'gauss'
# solution form
phi_2 = Form(func_space_2_lobatto)
phi_2.basis.quad_grid = 'gauss'
form_source = Form(func_space_2_lobatto)
form_source.discretize(source, ('gauss', 30))
# find inner product
M_1k = inner(basis_1, basis_1, mesh_k)
N_2 = inner(d(basis_1), basis_2)
M_2 = inner(basis_2, basis_2)
# assemble
M_1k = assemble(M_1k, func_space_1_lobatto)
N_2 = assemble(N_2, (func_space_1_lobatto, func_space_2_lobatto))
M_2 = assemble(M_2, func_space_2_lobatto)
lhs = sparse.bmat([[M_1k, N_2], [N_2.transpose(), None]]).tocsc()
rhs_source = (form_source.cochain @ M_2)[:, np.newaxis]
rhs_zeros = np.zeros(lhs.shape[0] - np.size(rhs_source))[:, np.newaxis]
rhs = np.vstack((rhs_zeros, rhs_source))
solution = sparse.linalg.spsolve(lhs, rhs)
phi_2.cochain = solution[-func_space_2_lobatto.num_dof:]
# sample the solution
xi = eta = np.linspace(-1, 1, 200)
phi_2.reconstruct(xi, eta)
(x, y), data = phi_2.export_to_plot()
plt.contourf(x, y, data)
plt.show()
print("max value {0} \nmin value {1}" .format(np.max(data), np.min(data)))
npt.assert_array_almost_equal(self.solution(x, y), data, decimal=2)
def test_inner(self):
list_cases = [
'p2_n2-2', 'p2_n3-2', 'p5_n1-10', 'p10_n2-2', 'p13_n12-8'
]
p = [2, 2, 5, 10, 13]
n = [(2, 2), (3, 2), (1, 10), (2, 2), (12, 8)]
curvature = [0.1, 0.1, 0.1, 0.1, 0.1]
for i, case in enumerate(list_cases[:-1]):
print("Test case n : ", i)
# basis = basis_forms.
# print("theo size ", (p[i] + 1)**2 *
# (p[i] + 1)**2 * n[i][0] * n[i][1])
M_2_ref = np.loadtxt(
os.getcwd() + '/src/tests/test_M_2/M_2_' + case + '.dat',
delimiter=',').reshape((p[i])**2, n[i][0] * n[i][1], (p[i])**2)
# print("actual size ", np.size(M_0_ref))
# print(np.shape(M_0_ref))
my_mesh = CrazyMesh(2,
n[i], ((-1, 1), (-1, 1)),
curvature=curvature[i])
function_space = FunctionSpace(my_mesh, '2-lobatto', p[i])
basis_0 = BasisForm(function_space)
basis_0.quad_grid = 'lobatto'
basis_1 = BasisForm(function_space)
basis_1.quad_grid = 'lobatto'
M_2 = inner(basis_0, basis_1)
# print("REF ------------------ \n", M_2_ref[:, 0, :])
# print("CALCULATED _----------------\n", M_2[:, :, 0])
for el in range(n[i][0] * n[i][1]):
npt.assert_array_almost_equal(M_2_ref[:, el, :],
M_2[:, :, el],
decimal=7)
def test_dual_space(self):
"""Test the generation of the dual space."""
p = 3, 3
mesh = CrazyMesh(2, (1, 1), ((-1, 1), (-1, 1)), curvature=0.2)
func_space = FunctionSpace(mesh, '0-lobatto', p)
dual_space_ref = FunctionSpace(mesh, '2-gauss', (p[0] - 1, p[1] - 1))
dual_space = DualSpace(func_space, extend=False)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '2-gauss', p)
dual_space_ref = FunctionSpace(mesh, '0-lobatto', (p[0] + 1, p[1] + 1))
dual_space = DualSpace(func_space, extend=False)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '0-gauss', p)
dual_space_ref = FunctionSpace(mesh, '2-lobatto', (p[0] + 1, p[1] + 1))
dual_space = DualSpace(func_space, extend=False)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '2-lobatto', p)
dual_space_ref = FunctionSpace(mesh, '0-gauss', (p[0] - 1, p[1] - 1))
dual_space = DualSpace(func_space, extend=False)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '1-lobatto', p)
dual_space_ref = FunctionSpace(mesh, '1-ext_gauss', (p[0] - 1, p[1] - 1))
dual_space = DualSpace(func_space, extend=True)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '1-ext_gauss', p)
dual_space_ref = FunctionSpace(mesh, '1-lobatto', (p[0] + 1, p[1] + 1))
dual_space = DualSpace(func_space, extend=True)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '1-lobatto', p)
dual_space_ref = FunctionSpace(mesh, '1-gauss', (p[0] - 1, p[1] - 1))
dual_space = DualSpace(func_space, extend=False)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
func_space = FunctionSpace(mesh, '1-gauss', p)
dual_space_ref = FunctionSpace(mesh, '1-lobatto', (p[0] + 1, p[1] + 1))
dual_space = DualSpace(func_space, extend=False)
self.assertEqual(dual_space_ref.form_type, dual_space.form_type,
msg="Form type is different")
self.assertEqual(dual_space_ref.p, dual_space.p)
def test_single_element(self):
"""Test the anysotropic case in a single element."""
dim = 2
elements_layout = (1, 1)
bounds_domain = ((-1, 1), (-1, 1))
curvature = 0.1
p = (20, 20)
is_inner = False
crazy_mesh = CrazyMesh(dim, elements_layout, bounds_domain, curvature)
func_space_2_lobatto = FunctionSpace(crazy_mesh, '2-lobatto', p, is_inner)
func_space_1_lobatto = FunctionSpace(crazy_mesh, '1-lobatto', p, is_inner)
def diffusion_11(x, y): return 4 * np.ones(np.shape(x))
def diffusion_12(x, y): return 3 * np.ones(np.shape(x))
def diffusion_22(x, y): return 5 * np.ones(np.shape(x))
mesh_k = MeshFunction(crazy_mesh)
mesh_k.continous_tensor = [diffusion_11, diffusion_12, diffusion_22]
basis_1 = BasisForm(func_space_1_lobatto)
basis_1.quad_grid = 'gauss'
basis_2 = BasisForm(func_space_2_lobatto)
basis_2.quad_grid = 'gauss'
phi_2 = Form(func_space_2_lobatto)
phi_2.basis.quad_grid = 'gauss'
M_1k = inner(basis_1, basis_1, mesh_k)
N_2 = inner(basis_2, d(basis_1))
def source(x, y):
return -36 * np.pi ** 2 * np.sin(2 * np.pi * x) * np.sin(2 * np.pi * y) + 24 * np.pi ** 2 * np.cos(2 * np.pi * x) * np.cos(2 * np.pi * y)
form_source = Form(func_space_2_lobatto)
form_source.discretize(source)
M_2 = inner(basis_2, basis_2)
lhs = np.vstack((np.hstack((M_1k[:, :, 0], N_2[:, :, 0])), np.hstack(
(np.transpose(N_2[:, :, 0]), np.zeros((np.shape(N_2)[1], np.shape(N_2)[1]))))))
rhs = np.zeros((np.shape(lhs)[0], 1))
rhs[-np.shape(M_2)[0]:] = form_source.cochain @ M_2
phi_2.cochain = np.linalg.solve(lhs, rhs)[-phi_2.basis.num_basis:].flatten()
xi = eta = np.linspace(-1, 1, 200)
phi_2.reconstruct(xi, eta)
(x, y), data = phi_2.export_to_plot()
print("max value {0} \nmin value {1}" .format(np.max(data), np.min(data)))
npt.assert_array_almost_equal(self.solution(x, y), data, decimal=2)
def test_local_to_global_cochain(self):
# TODO: currently not supported px != py
"""Test local to global mapping of cochians."""
mesh = CrazyMesh(2, (2, 2), ((-1, 1), (-1, 1)), curvature=0.3)
cases = ['2-lobatto', '2-gauss']
p = 2, 3
for form_case in cases:
func_space = FunctionSpace(mesh, form_case, p)
form_2 = Form(func_space)
form_2.discretize(paraboloid)
def test_ext_gauss_projection(self):
p = (10, 10)
n = (5, 6)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
func_space_extGau = FunctionSpace(mesh, '0-ext_gauss', p)
form_0_extG = ExtGaussForm_0(func_space_extGau)
form_0_extG.discretize(self.pfun)
xi = eta = np.linspace(-1, 1, 20)
form_0_extG.reconstruct(xi, eta)
(x, y), data = form_0_extG.export_to_plot()
npt.assert_array_almost_equal(self.pfun(x, y), data)
def test_lobatto_projection(self):
p = (10, 10)
n = (5, 6)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
func_space = FunctionSpace(mesh, '0-lobatto', p)
form_0 = Form(func_space)
form_0.discretize(self.pfun)
xi = eta = np.linspace(-1, 1, 20)
form_0.reconstruct(xi, eta)
(x, y), data = form_0.export_to_plot()
npt.assert_array_almost_equal(self.pfun(x, y), data)
def test_weighted_inner_continous(self):
"""Test for weighted inner product."""
mesh = CrazyMesh(2, (2, 2), ((-1, 1), (-1, 1)), curvature=0.2)
func_space = FunctionSpace(mesh, '1-lobatto', (3, 4))
basis = BasisForm(func_space)
basis.quad_grid = 'gauss'
K = MeshFunction(mesh)
K.continous_tensor = [diff_tens_11, diff_tens_12, diff_tens_22]
M_1_weighted = inner(basis, basis, K)
M_1 = inner(basis, basis)
npt.assert_array_almost_equal(M_1, M_1_weighted)
def test_l2_norm(self):
p = (10, 10)
n = (10, 10)
mesh = CrazyMesh(2, n, ((0, 1), (0, 1)), 0.1)
func_space = FunctionSpace(mesh, '1-lobatto', p)
form_1 = Form(func_space)
form_1.discretize((self.ufun_x, self.ufun_y))
# print("chochain : \n", form_1.chochain)
error_global, error_local = form_1.l_2_norm((self.ufun_x, self.ufun_y))
self.assertLess(error_global, 4 * 10**(-12))
self.assertLess(error_local, 4 * 10**(-10))
def test_discretize_simple(self):
"""Simple discretization of 0 forms."""
p_s = [(2, 2)]
n = (2, 2)
for p in p_s:
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.0)
func_space = FunctionSpace(mesh, '0-lobatto', p)
form_0 = Form(func_space)
form_0.discretize(self.pfun)
# values at x = +- 0.5 and y = +- 0.5
ref_value = np.array((1, -1, -1, 1))
npt.assert_array_almost_equal(ref_value, form_0.cochain_local[4])
def test_projection_gauss(self):
p = (10, 10)
n = (5, 6)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.1)
func_space = FunctionSpace(mesh, '1-gauss', p)
form_1 = Form(func_space)
form_1.discretize((self.ufun_x, self.ufun_y))
xi = eta = np.linspace(-1, 1, 40)
form_1.reconstruct(xi, eta)
(x, y), data_dx, data_dy = form_1.export_to_plot()
npt.assert_array_almost_equal(self.ufun_x(x, y), data_dx, decimal=4)
npt.assert_array_almost_equal(self.ufun_y(x, y), data_dy, decimal=4)
def test_projection_gauss(self):
def ffun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (20, 20)
n = (3, 3)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
func_space = FunctionSpace(mesh, '2-ext_gauss', p)
f2eg = Form(func_space)
f2eg.discretize(ffun)
xi = eta = np.linspace(-1, 1, 50)
f2eg.reconstruct(xi, eta)
(x, y), data = f2eg.export_to_plot()
npt.assert_array_almost_equal(ffun(x, y), data)
def test_exceptions(self):
p = 2
mesh = CrazyMesh(2, (2, 2), ((-1, 1), (-1, 1)))
func_space = FunctionSpace(mesh, '1-lobatto', p)
basis = BasisForm(func_space)
basis_1 = BasisForm(func_space)
quad_cases = [(None, 'gauss'), (None, None), ('gauss', None), ('lobatto', 'gauss')]
for case in quad_cases:
if None in case:
with self.assertRaises(UnboundLocalError):
basis.quad_grid = case[0]
basis_1.quad_grid = case[1]
else:
basis.quad_grid = case[0]
basis_1.quad_grid = case[1]
self.assertRaises(QuadratureError, inner, basis, basis_1)
def test_reconstruct_lobatto(self):
"""Test the reconstructin of lobatto forms."""
p = (20, 20)
n = (3, 2)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
xi = eta = np.linspace(-1, 1, 30)
func_space = FunctionSpace(mesh, '2-lobatto', p)
form_2 = Form(func_space)
cochain = np.loadtxt(
'src/tests/test_form_2/cochain_lobatto_n3-2_p20-20_c3.dat',
delimiter=',')
ref_reconstructed = np.loadtxt(
'src/tests/test_form_2/reconstructed_lobatto_n3-2_p20-20_c3_xieta_30.dat',
delimiter=',')
form_2.cochain = cochain
form_2.reconstruct(xi, eta)
npt.assert_array_almost_equal(ref_reconstructed, form_2.reconstructed)
def test_reduction_visualization_extended_gauss_2form(self):
def ffun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (20, 20)
n = (3, 3)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
func_space = FunctionSpace(mesh, '2-ext_gauss', p)
f2eg = Form(func_space)
f2eg.discretize(ffun)
xi = eta = np.linspace(-1, 1, 50)
f2eg.reconstruct(xi, eta)
(x, y), data = f2eg.export_to_plot()
plt.contourf(x, y, data)
plt.title('reduced extened_gauss 2-form')
plt.colorbar()
plt.show()
def test_discretize_lobatto(self):
def func_x(x, y):
return np.ones(np.shape(x))
def func_y(x, y):
return np.ones(np.shape(x)) * 2
mesh = CrazyMesh(2, (2, 2), ((-1, 1), (-1, 1)), 0.3)
func_space = FunctionSpace(mesh, '1-lobatto', (3, 3))
form_1 = Form(func_space)
form_1.discretize((func_x, func_y))
cochain_local_ref = np.loadtxt(
'src/tests/test_discrete_1_form/discrete_1_form_dx_1_dy_2.csv',
delimiter=',')
npt.assert_array_almost_equal(form_1.cochain_local,
cochain_local_ref,
decimal=3)
def test_coboundary_lobatto_e10_inner(self):
"""Test of the coundary 0->1 for lobatto form inner oriented."""
p = (20, 20)
n = (6, 6)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.1)
xi = eta = np.linspace(-1, 1, 100)
func_space = FunctionSpace(mesh, '0-lobatto', p)
form_0 = Form(func_space)
form_0.discretize(self.pfun)
form_1 = d(form_0)
form_1.reconstruct(xi, eta)
(x, y), data_dx, data_dy = form_1.export_to_plot()
ufun_x, ufun_y = self.ufun()
npt.assert_array_almost_equal(ufun_x(x, y), data_dx)
npt.assert_array_almost_equal(ufun_y(x, y), data_dy)
def test_reduction_visualization_lobatto_2form(self):
def ffun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (20, 20)
n = (2, 2)
mesh = CrazyMesh(2, n, ((-1.25, 1), (-1.25, 1)), 0.3)
xi = eta = np.linspace(-1, 1, 30)
func_space = FunctionSpace(mesh, '2-lobatto', p)
form_2 = Form(func_space)
form_2.discretize(ffun)
# np.savetxt('cochain_lobatto_n3-2_p20-20_c3.dat', form_2.cochain, delimiter=',')
form_2.reconstruct(xi, eta)
(x, y), data = form_2.export_to_plot()
plt.contourf(x, y, data)
plt.title('our reduced lobatto 2-form')
plt.colorbar()
plt.show()
def test_metric(self):
def gamma1(s):
return 2 * s - 1, -1 * np.ones(np.shape(s))
def gamma2(t):
return 1 * np.ones(np.shape(t)), 2 * t - 1
def gamma3(s):
return 2 * s - 1, 1 * np.ones(np.shape(s))
def gamma4(t):
return -1 * np.ones(np.shape(t)), 2 * t - 1
def dgamma1(s):
return 2 * np.ones(np.shape(s)), 0 * np.ones(np.shape(s))
def dgamma2(t):
return 0 * np.ones(np.shape(t)), 2 * np.ones(np.shape(t))
def dgamma3(s):
return 2 * np.ones(np.shape(s)), 0 * np.ones(np.shape(s))
def dgamma4(t):
return 0 * np.ones(np.shape(t)), 2 * np.ones(np.shape(t))
gamma = (gamma1, gamma2, gamma3, gamma4)
dgamma = (dgamma1, dgamma2, dgamma3, dgamma4)
sand_shale_mesh = TransfiniteMesh(2, (1, 1), gamma, dgamma)
crazy_mesh = CrazyMesh(2, (1, 1), ((-1, 1), (-1, 1)))
xi = eta = np.linspace(-1, 1, 5)
npt.assert_array_almost_equal(crazy_mesh.dx_dxi(xi, eta),
sand_shale_mesh.dx_dxi(xi, eta))
npt.assert_array_almost_equal(crazy_mesh.dx_deta(xi, eta),
sand_shale_mesh.dx_deta(xi, eta))
npt.assert_array_almost_equal(crazy_mesh.dy_dxi(xi, eta),
sand_shale_mesh.dy_dxi(xi, eta))
npt.assert_array_almost_equal(crazy_mesh.dy_deta(xi, eta),
sand_shale_mesh.dy_deta(xi, eta))
npt.assert_array_almost_equal(crazy_mesh.g(xi, eta),
sand_shale_mesh.g(xi, eta))
def test_coboundary_extended_gauss_e10_inner(self):
def pfun(x, y):
return np.sin(np.pi * x) * np.sin(np.pi * y)
p = (10, 10)
n = (20, 20)
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0.3)
func_space_extGau = FunctionSpace(mesh, '0-ext_gauss', p)
form_0_extG = Form(func_space_extGau)
form_0_extG.discretize(self.pfun)
xi = eta = np.linspace(-1, 1, 10)
form_0_extG.reconstruct(xi, eta)
form_1 = d(form_0_extG)
form_1.reconstruct(xi, eta)
(x, y), data_dx, data_dy = form_1.export_to_plot()
ufun_x, ufun_y = self.ufun()
npt.assert_array_almost_equal(ufun_x(x, y), data_dx)
npt.assert_array_almost_equal(ufun_y(x, y), data_dy)
print(np.min(data_dy))
def test_inner(self):
"""Test inner product of one forms."""
list_cases = ['p2_n2-2', 'p2_n3-2',
'p5_n1-10', 'p10_n2-2', 'p13_n12-8']
p = [2, 2, 5, 10, 13]
n = [(2, 2), (3, 2), (1, 10), (2, 2), (12, 8)]
curvature = [0.1, 0.1, 0.1, 0.1, 0.1]
for i, case in enumerate(list_cases[:-1]):
M_1_ref = np.loadtxt(
os.getcwd() + '/src/tests/test_M_1/M_1k_' + case + '.dat', delimiter=',').reshape(2 * p[i] * (p[i] + 1), n[i][0] * n[i][1], 2 * p[i] * (p[i] + 1))
my_mesh = CrazyMesh(
2, n[i], ((-1, 1), (-1, 1)), curvature=curvature[i])
function_space = FunctionSpace(my_mesh, '1-lobatto', p[i])
form = BasisForm(function_space)
form.quad_grid = 'gauss'
form_1 = BasisForm(function_space)
form_1.quad_grid = 'gauss'
K = MeshFunction(my_mesh)
K.continous_tensor = [diff_tens_11, diff_tens_12, diff_tens_22]
M_1 = inner(form, form_1, K)
for el in range(n[i][0] * n[i][1]):
npt.assert_array_almost_equal(
M_1_ref[:, el, :], M_1[:, :, el])
def test_reduction_visualization_lobatto_1form(self):
"""Simple discretization of 1 forms."""
p_s = [(10, 10)]
n = (2, 2)
for p in p_s:
mesh = CrazyMesh(2, n, ((-1, 1), (-1, 1)), 0)
func_space = FunctionSpace(mesh, '1-lobatto', p)
form_1 = Form(func_space)
form_1.discretize((self.ufun_x, self.ufun_y))
print(form_1.function_space.dof_map.dof_map)
xi = eta = np.linspace(-1, 1, 40)
form_1.reconstruct(xi, eta)
(x, y), data_dx, data_dy = form_1.export_to_plot()
plt.contourf(x, y, data_dx)
plt.title('projected lobatto 1-form dx')
plt.colorbar()
plt.show()
plt.contourf(x, y, data_dy)
plt.title('projected lobatto 1-form dy')
plt.colorbar()
plt.show()
print(np.min(data_dy))
def ffun(x, y):
return -2 * np.pi**2 * np.sin(np.pi * x) * np.sin(np.pi * y)
# %% define
p = 0
n = 2
c = 0.0
px = py = p
nx = ny = n
print("\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^")
print("Start div grad solver @ p=", px)
print(" @ n=", nx)
print(" @ c=", c)
mesh = CrazyMesh(2, (nx, ny), ((-1, 1), (-1, 1)), c)
xi = eta = np.linspace(-1, 1, np.ceil(500 / (nx * ny)) + 1)
# %% function spaces
func_space_eg0 = FunctionSpace(mesh, '0-ext_gauss', (px, py))
p0 = Form(func_space_eg0)
p0_exact = Form(func_space_eg0)
p0_exact.discretize(pfun)
#p0_exact.reconstruct(xi, eta)
#(x, y), data = p0_exact.export_to_plot()
#plt.contourf(x, y, data)
#plt.title('exact extended gauss 0-form, p0')
#plt.colorbar()
#plt.show()
#func_space_g0 = FunctionSpace(mesh, '0-gauss', (px, py))
# %%
func_space_eg1 = FunctionSpace(mesh, '1-ext_gauss', (px, py))
