def test_poisson_solver_spherical():
"""test the poisson solver on Polar grids"""
for grid in [SphericalSymGrid(4, 8), SphericalSymGrid([2, 4], 8)]:
for bc_val in ["auto_periodic_neumann", {"value": 1}]:
bcs = grid.get_boundary_conditions(bc_val)
d = ScalarField.random_uniform(grid)
d -= d.average # balance the right hand side
sol = solve_poisson_equation(d, bcs)
test = sol.laplace(bcs)
np.testing.assert_allclose(
test.data, d.data, err_msg=f"bcs={bc_val}, grid={grid}", rtol=1e-6
)
def test_poisson_solver_polar():
"""test the poisson solver on Polar grids"""
for grid in [PolarSymGrid(4, 8), PolarSymGrid([2, 4], 8)]:
for bc_val in ["natural", {"value": 1}]:
bcs = grid.get_boundary_conditions(bc_val)
d = ScalarField.random_uniform(grid)
d -= d.average # balance the right hand side
sol = solve_poisson_equation(d, bcs)
test = sol.laplace(bcs)
msg = f"grid={grid}, bcs={bc_val}"
np.testing.assert_allclose(test.data,
d.data,
err_msg=msg,
rtol=1e-6)
"""
Solving Poisson's equation in 1d
================================
This example shows how to solve a 1d Poisson equation with boundary conditions.
"""
from pde import CartesianGrid, ScalarField, solve_poisson_equation
grid = CartesianGrid([[0, 1]], 32, periodic=False)
field = ScalarField(grid, 1)
result = solve_poisson_equation(field, bc=[{"value": 0}, {"derivative": 1}])
result.plot()
"""
Solving Poisson's equation in 1d
================================
This example shows how to solve a 1d Poisson equation with boundary conditions.
"""
from pde import CartesianGrid, ScalarField, solve_poisson_equation
grid = CartesianGrid([[0, 1]], 32, periodic=False)
field = ScalarField(grid, 1)
result = solve_poisson_equation(field, bc=[{'value': 0}, {'derivative': 1}])
result.plot()