def test_poisson_solver_1d():
""" test the poisson solver on 1d grids """
# solve Laplace's equation
grid = UnitGrid([4])
field = ScalarField(grid)
res = field.solve_poisson([{"value": -1}, {"value": 3}])
np.testing.assert_allclose(res.data, grid.axes_coords[0] - 1)
res = field.solve_poisson([{"value": -1}, {"derivative": 1}])
np.testing.assert_allclose(res.data, grid.axes_coords[0] - 1)
# test Poisson equation with 2nd Order BC
res = field.solve_poisson([{"value": -1}, "extrapolate"])
# solve Poisson's equation
grid = CartesianGrid([[0, 1]], 4)
field = ScalarField(grid, data=1)
res = field.copy()
field.solve_poisson([{"value": 1}, {"derivative": 1}], out=res)
xs = grid.axes_coords[0]
np.testing.assert_allclose(res.data, 1 + 0.5 * xs**2, rtol=1e-2)
# test inconsistent problem
field.data = 1
with pytest.raises(RuntimeError, match="Neumann"):
field.solve_poisson({"derivative": 0})
def test_poisson_solver_2d():
""" test the poisson solver on 2d grids """
grid = CartesianGrid([[0, 2 * np.pi]] * 2, 16)
bcs = [{"value": "sin(y)"}, {"value": "sin(x)"}]
# solve Laplace's equation
field = ScalarField(grid)
res = field.solve_poisson(bcs)
xs = grid.cell_coords[..., 0]
ys = grid.cell_coords[..., 1]
# analytical solution was obtained with Mathematica
expect = (np.cosh(np.pi - ys) * np.sin(xs) +
np.cosh(np.pi - xs) * np.sin(ys)) / np.cosh(np.pi)
np.testing.assert_allclose(res.data, expect, atol=1e-2, rtol=1e-2)
# test more complex case for exceptions
res = field.solve_poisson([{"value": "sin(y)"}, {"curvature": "sin(x)"}])