def test_solve_spherical_system():
# a PDE system that can be decoupled into 2 Laplacian equations :math:`\\nabla^2 u = 0` and :math:`\\nabla^2 v = 0`
pde_system = lambda u, v, r, theta, phi: [
laplacian_spherical(u, r, theta, phi) + laplacian_spherical(
v, r, theta, phi),
laplacian_spherical(u, r, theta, phi) - laplacian_spherical(
v, r, theta, phi),
]
# constant boundary conditions for u and v; solution should be u = 0 identically and v = 1 identically
conditions = [
DirichletBVPSpherical(r_0=0.,
f=lambda phi, theta: 0.,
r_1=1.,
g=lambda phi, theta: 0.),
DirichletBVPSpherical(r_0=0.,
f=lambda phi, theta: 1.,
r_1=1.,
g=lambda phi, theta: 1.),
]
with pytest.warns(FutureWarning):
solution, _ = solve_spherical_system(pde_system,
conditions,
0.0,
1.0,
max_epochs=2,
return_best=True)
assert isinstance(solution, SolutionSpherical)
def test_solve_spherical_system():
# a PDE system that can be decoupled into 2 Laplacian equations :math:`\\nabla^2 u = 0` and :math:`\\nabla^2 v = 0`
pde_system = lambda u, v, r, theta, phi: [
laplacian_spherical(u, r, theta, phi) + laplacian_spherical(
v, r, theta, phi),
laplacian_spherical(u, r, theta, phi) - laplacian_spherical(
v, r, theta, phi),
]
# constant boundary conditions for u and v; solution should be u = 0 identically and v = 1 identically
conditions = [
DirichletBVPSpherical(r_0=0.,
f=lambda phi, theta: 0.,
r_1=1.,
g=lambda phi, theta: 0.),
DirichletBVPSpherical(r_0=0.,
f=lambda phi, theta: 1.,
r_1=1.,
g=lambda phi, theta: 1.),
]
solution, loss_history = solve_spherical_system(pde_system,
conditions,
0.0,
1.0,
max_epochs=2,
return_best=True)
generator = GeneratorSpherical(512, r_min=0., r_max=1.)
rs, thetas, phis = generator.get_examples()
us, vs = solution(rs, thetas, phis, as_type='np')
def test_solve_spherical_system():
# a PDE system that can be decoupled into 2 Laplacian equations :math:`\\nabla^2 u = 0` and :math:`\\nabla^2 v = 0`
pde_system = lambda u, v, r, theta, phi: [
laplacian_spherical(u, r, theta, phi) + laplacian_spherical(
v, r, theta, phi),
laplacian_spherical(u, r, theta, phi) - laplacian_spherical(
v, r, theta, phi),
]
# constant boundary conditions for u and v; solution should be u = 0 identically and v = 1 identically
conditions = [
DirichletBVPSpherical(r_0=0.,
f=lambda phi, theta: 0.,
r_1=1.,
g=lambda phi, theta: 0.),
DirichletBVPSpherical(r_0=0.,
f=lambda phi, theta: 1.,
r_1=1.,
g=lambda phi, theta: 1.),
]
solution, loss_history = solve_spherical_system(pde_system,
conditions,
0.0,
1.0,
max_epochs=500,
return_best=True)
generator = ExampleGeneratorSpherical(512, r_min=0., r_max=1.)
rs, thetas, phis = generator.get_examples()
us, vs = solution(rs, thetas, phis, as_type='np')
assert np.isclose(us, np.zeros(512),
atol=0.005).all(), f"Solution u is not straight 0s: {us}"
assert np.isclose(vs, np.ones(512),
atol=0.005).all(), f"Solution v is not straight 1s: {vs}"
print("solve_spherical_system tests passed")