def computeGrid(DIMS, HermCheb, FourCheb, ChebCol):
# Get the domain dimensions
L1 = DIMS[0]
L2 = DIMS[1]
ZH = DIMS[2]
NX = DIMS[3]
NZ = DIMS[4]
if ChebCol:
# Compute the Chebyshev native grids
xi, wcp = cheblb(NZ) #[-1 +1]
z = 0.5 * ZH * (1.0 + xi)
else:
z = np.linspace(0.0, ZH, num=NZ, endpoint=True)
# Map reference 1D domains to physical 1D domains
if HermCheb and not FourCheb:
alpha, whf = hefunclb(NX) #(-inf inf)
x = 0.5 * abs(L2 - L1) / np.amax(alpha) * alpha
elif FourCheb and not HermCheb:
x = np.linspace(L1, L2, num=NX+1, endpoint=True)
else:
alpha, whf = hefunclb(NX) #(-inf inf)
x = 0.5 * abs(L2 - L1) / np.amax(alpha) * alpha
# Return the REFS structure
REFS = [x, z]
return REFS
def computeChebyshevDerivativeMatrix(DIMS):
# Get data from DIMS
ZH = DIMS[2]
NZ = DIMS[4]
# Make a truncation index
tdex = np.array(range(NZ-1), dtype=int)
# Initialize grid and make column vector
xi, wcp = cheblb(NZ)
# Get the Chebyshev transformation matrix
CTD = chebpolym(NZ-1, -xi)
# Make a diagonal matrix of weights
W = np.diag(wcp)
# Compute scaling for the forward transform
S = np.eye(NZ)
for ii in range(NZ - 1):
temp = W.dot(CTD[:,ii])
temp = ((CTD[:,ii]).T).dot(temp)
S[ii,ii] = temp ** (-1)
S[NZ-1,NZ-1] = 1.0 / mt.pi
# Compute the spectral derivative coefficients
SDIFF = np.zeros((NZ,NZ))
SDIFF[NZ-2,NZ-1] = 2.0 * NZ
for ii in reversed(range(NZ - 2)):
A = 2.0 * (ii + 1)
B = 1.0
if ii > 0:
c = 1.0
else:
c = 2.0
SDIFF[ii,:] = B / c * SDIFF[ii+2,:]
SDIFF[ii,ii+1] = A / c
# Chebyshev spectral transform in matrix form
temp = (CTD[:,tdex].T).dot(W)
STR_C = S[np.ix_(tdex,tdex)].dot(temp);
# Chebyshev spatial derivative based on spectral differentiation
# Domain scale factor included here
temp = (CTD[:,tdex]).dot(SDIFF[np.ix_(tdex,tdex)])
DDMT = - (2.0 / ZH) * temp.dot(STR_C);
# Output the complete matrices as well
temp = CTD.dot(W)
STR_C = S.dot(temp);
# Chebyshev spatial derivative based on spectral differentiation
# Domain scale factor included here
temp = CTD.dot(SDIFF)
DDMF = - (2.0 / ZH) * temp.dot(STR_C);
return DDMF, DDMT, STR_C
def computeChebyshevDerivativeMatrix_X(DIMS):
# Get data from DIMS
#ZH = DIMS[2]
#NZ = DIMS[4]
# Get data from DIMS
L1 = DIMS[0]
L2 = DIMS[1]
NX = DIMS[3]
ZH = abs(L2 - L1)
NZ = NX + 1
# Initialize grid and make column vector
xi, wcp = cheblb(NZ)
# Get the Chebyshev transformation matrix
CTD = chebpolym(NZ-1, -xi)
# Make a diagonal matrix of weights
W = np.diag(wcp)
# Compute scaling for the forward transform
S = np.eye(NZ)
for ii in range(NZ - 1):
temp = W.dot(CTD[:,ii])
temp = ((CTD[:,ii]).T).dot(temp)
S[ii,ii] = temp ** (-1)
S[NZ-1,NZ-1] = 1.0 / mt.pi
# Compute the spectral derivative coefficients
SDIFF = np.zeros((NZ,NZ))
SDIFF[NZ-2,NZ-1] = 2.0 * NZ
for ii in reversed(range(NZ - 2)):
A = 2.0 * (ii + 1)
B = 1.0
if ii > 0:
c = 1.0
else:
c = 2.0
SDIFF[ii,:] = B / c * SDIFF[ii+2,:]
SDIFF[ii,ii+1] = A / c
# Chebyshev spectral transform in matrix form
temp = CTD.dot(W)
STR_C = S.dot(temp);
# Chebyshev spatial derivative based on spectral differentiation
# Domain scale factor included here
temp = (CTD).dot(SDIFF)
DDM = - (2.0 / ZH) * temp.dot(STR_C);
return DDM, STR_C
def computeGrid(DIMS):
# Get the domain dimensions
L1 = DIMS[0]
L2 = DIMS[1]
ZH = DIMS[2]
NX = DIMS[3]
NZ = DIMS[4]
# Compute the Hermite function and Chebyshev native grids
alpha, whf = hefunclb(NX + 1) #(-inf inf)
xi, wcp = cheblb(NZ) #[-1 +1]
# Map reference 1D domains to physical 1D domains
x = 0.5 * abs(L2 - L1) / np.amax(alpha) * alpha
z = 0.5 * ZH * (1.0 + xi)
# Return the REFS structure
REFS = [x, z]
return REFS