comm = MPI.COMM_WORLD num_processes = comm.Get_size() rank = comm.Get_rank() Np = N / num_processes # Get points and weights for Chebyshev weighted integrals quad = "GC" BC1 = array([1,0,0, 1,0,0]) BC2 = array([0,1,0, 0,1,0]) BC3 = array([0,1,0, 1,0,0]) SC = ChebyshevTransform(quad) ST = ShenBasis(BC1, quad) SN = ShenBasis(BC2, quad, Neumann = True) SR = ShenBasis(BC3, quad) SB = ShenBiharmonicBasis(quad, fast_transform=False) points, weights = ST.points_and_weights(N[0]) pointsN, weightsN = SN.points_and_weights(N[0]) x1 = arange(N[1], dtype=float)*L[1]/N[1] x2 = arange(N[2], dtype=float)*L[2]/N[2] # Get grid for velocity points X = array(meshgrid(points[rank*Np[0]:(rank+1)*Np[0]], x1, x2, indexing='ij'), dtype=float) Y = array(meshgrid(pointsN[rank*Np[0]:(rank+1)*Np[0]], x1, x2, indexing='ij'), dtype=float) Nf = N[2]/2+1 # Number of independent complex wavenumbers in z-direction Nu = N[0]-2 # Number of velocity modes in Shen basis U = empty((3, Np[0], N[1], N[2])) U_hat = empty((3, N[0], Np[1], Nf), dtype="complex") P = empty((Np[0], N[1], N[2]))
M = 2 ** 3
quad = "GL"
BC1 = array([1, 0, 0, 1, 0, 0])
BC2 = array([0, 1, 0, 0, 1, 0])
BC3 = array([0, 1, 0, 1, 0, 0])
SC = ChebyshevTransform(quad)
ST = ShenBasis(BC1, quad)
SN = ShenBasis(BC2, quad, Neumann=True)
SR = ShenBasis(BC3, quad)
SB = ShenBiharmonicBasis(quad, fast_transform=False)
if test == "0":
v_exact = zeros(M)
f = zeros(M)
points, weights = SN.points_and_weights(M)
f[:] = (-8.0 / 3.0) * points # -((pi/2.)**2)*sin(pi*points/2.)
v_exact = -(4.0 / 9.0) * (points ** 3 - 3.0 * points) # sin(pi*points/2.)
v = Poisson1DNeumann(M, f, quad, SC, SN, BC2)
print "Error: ", linalg.norm(v - v_exact, inf)
assert allclose(v, v_exact)
pl.plot(points, v_exact, points, v)
pl.show()
elif test == "1":
v_exact = zeros(M)
f = zeros(M)
points, weights = ST.points_and_weights(M)
f[:] = -4.0
v_exact = 2 * (1.0 - points ** 2)
v = Poisson1D(M, f, quad, SC, ST, BC1)