def __init__(self, N, alfa, quad="GL", neumann=False):
# Prepare LU Helmholtz solver for velocity
self.N = N
self.alfa = alfa
self.neumann = neumann
M = (N - 4) / 2 if neumann else (N - 3) / 2
if hasattr(alfa, "__len__"):
Ny, Nz = alfa.shape
self.u0 = zeros((2, M + 1, Ny, Nz), float) # Diagonal entries of U
self.u1 = zeros((2, M, Ny, Nz), float) # Diagonal+1 entries of U
self.u2 = zeros((2, M - 1, Ny, Nz),
float) # Diagonal+2 entries of U
self.L = zeros((2, M, Ny, Nz),
float) # The single nonzero row of L
self.s = slice(1, N - 2) if neumann else slice(0, N - 2)
SFTc.LU_Helmholtz_3D(N, neumann, quad == "GL", self.alfa, self.u0,
self.u1, self.u2, self.L)
else:
self.u0 = zeros((2, M + 1), float) # Diagonal entries of U
self.u1 = zeros((2, M), float) # Diagonal+1 entries of U
self.u2 = zeros((2, M - 1), float) # Diagonal+2 entries of U
self.L = zeros((2, M), float) # The single nonzero row of L
self.s = slice(1, N - 2) if neumann else slice(0, N - 2)
SFTc.LU_Helmholtz_1D(N, neumann, quad == "GL", self.alfa, self.u0,
self.u1, self.u2, self.L)
ck = ones(N[0] - 3)
if SN.quad == "GL": ck[-1] = 2
a0N = ones(N[0] - 5) * (-pi / 2) * (kk[1:-2] / (kk[1:-2] + 2))**2
b0N = pi / 2 * (1 + ck * (kk[1:] / (kk[1:] + 2))**4)
c0N = a0N.copy()
bcN = b0N.copy()
# Prepare LU Helmholtz solver for velocity
M = (N[0] - 3) / 2
u0 = zeros((2, M + 1, U_hat.shape[2], U_hat.shape[3])) # Diagonal entries of U
u1 = zeros((2, M, U_hat.shape[2], U_hat.shape[3])) # Diagonal+1 entries of U
u2 = zeros(
(2, M - 1, U_hat.shape[2], U_hat.shape[3])) # Diagonal+2 entries of U
L0 = zeros(
(2, M, U_hat.shape[2], U_hat.shape[3])) # The single nonzero row of L
SFTc.LU_Helmholtz_3D(N[0], 0, ST.quad == "GL", alfa1, u0, u1, u2, L0)
# Prepare LU Helmholtz solver Neumann for pressure
MN = (N[0] - 4) / 2
u0N = zeros(
(2, MN + 1, U_hat.shape[2], U_hat.shape[3])) # Diagonal entries of U
u1N = zeros((2, MN, U_hat.shape[2], U_hat.shape[3])) # Diagonal+1 entries of U
u2N = zeros(
(2, MN - 1, U_hat.shape[2], U_hat.shape[3])) # Diagonal+2 entries of U
LN = zeros(
(2, MN, U_hat.shape[2], U_hat.shape[3])) # The single nonzero row of L
SFTc.LU_Helmholtz_3D(N[0], 1, SN.quad == "GL", alfa2, u0N, u1N, u2N, LN)
def solvePressure(P_hat, U_hat):
global F_tmp, F_tmp2
