def build_FFF(N, dealias, dtype):
c = d3.CartesianCoordinates('x', 'y', 'z')
d = d3.Distributor(c, dtype=dtype)
if dtype == np.complex128:
xb = d3.ComplexFourier(c.coords[0],
size=N,
bounds=(0, Lx),
dealias=dealias)
yb = d3.ComplexFourier(c.coords[1],
size=N,
bounds=(0, Ly),
dealias=dealias)
zb = d3.ComplexFourier(c.coords[2],
size=N,
bounds=(0, Lz),
dealias=dealias)
elif dtype == np.float64:
xb = d3.RealFourier(c.coords[0],
size=N,
bounds=(0, Lx),
dealias=dealias)
yb = d3.RealFourier(c.coords[1],
size=N,
bounds=(0, Ly),
dealias=dealias)
zb = d3.RealFourier(c.coords[2],
size=N,
bounds=(0, Lz),
dealias=dealias)
b = (xb, yb, zb)
x = xb.local_grid(dealias)
y = yb.local_grid(dealias)
z = zb.local_grid(dealias)
r = (x, y, z)
return c, d, b, r
def test_poisson_1d_fourier(Nx, dtype, matrix_coupling):
# Bases
coord = d3.Coordinate('x')
dist = d3.Distributor(coord, dtype=dtype)
if dtype == np.complex128:
basis = d3.ComplexFourier(coord, size=Nx, bounds=(0, 2 * np.pi))
elif dtype == np.float64:
basis = d3.RealFourier(coord, size=Nx, bounds=(0, 2 * np.pi))
x = basis.local_grid(1)
# Fields
u = dist.Field(name='u', bases=basis)
g = dist.Field(name='c')
# Substitutions
dx = lambda A: d3.Differentiate(A, coord)
integ = lambda A: d3.Integrate(A, coord)
F = dist.Field(bases=basis)
F['g'] = -np.sin(x)
# Problem
problem = d3.LBVP([u, g], namespace=locals())
problem.add_equation("dx(dx(u)) + g = F")
problem.add_equation("integ(u) = 0")
# Solver
solver = problem.build_solver(matrix_coupling=[matrix_coupling])
solver.solve()
# Check solution
u_true = np.sin(x)
assert np.allclose(u['g'], u_true)