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 computeHermiteFunctionDerivativeMatrix(DIMS):
# Get data from DIMS
L1 = DIMS[0]
L2 = DIMS[1]
NX = DIMS[3]
alpha, whf = hefunclb(NX)
HT = hefuncm(NX, alpha, True)
HTD = hefuncm(NX+1, alpha, True)
# Get the scale factor
b = (np.amax(alpha) - np.min(alpha)) / abs(L2 - L1)
# Make a diagonal matrix of weights
W = np.diag(whf, k=0)
# Compute the coefficients of spectral derivative in matrix form
SDIFF = np.zeros((NX+2,NX+1));
SDIFF[0,1] = mt.sqrt(0.5)
SDIFF[NX,NX-1] = -mt.sqrt(NX * 0.5);
SDIFF[NX+1,NX] = -mt.sqrt((NX + 1) * 0.5);
for rr in range(1,NX):
SDIFF[rr,rr+1] = mt.sqrt((rr + 1) * 0.5);
SDIFF[rr,rr-1] = -mt.sqrt(rr * 0.5);
# Hermite function spectral transform in matrix form
STR_H = (HT.T).dot(W)
# Hermite function spatial derivative based on spectral differentiation
temp = (HTD).dot(SDIFF)
temp = temp.dot(STR_H)
DDM = b * temp
return DDM, STR_H
def computeHermiteFunctionDerivativeMatrix(DIMS):
# Get data from DIMS
L1 = DIMS[0]
L2 = DIMS[1]
NX = DIMS[3]
# Make a truncation index
tdex = np.array(range(NX - 1), dtype=int)
alpha, whf = hefunclb(NX + 1)
HT = hefuncm(NX, alpha, True)
HTD = hefuncm(NX + 1, alpha, True)
# Get the scale factor
b = (np.amax(alpha) - np.min(alpha)) / abs(L2 - L1)
# Make a diagonal matrix of weights
W = np.diag(whf, k=0)
# Compute the coefficients of spectral derivative in matrix form
SDIFF = np.zeros((NX + 2, NX + 1))
SDIFF[0, 1] = mt.sqrt(0.5)
SDIFF[NX, NX - 1] = -mt.sqrt(NX * 0.5)
SDIFF[NX + 1, NX] = -mt.sqrt((NX + 1) * 0.5)
for rr in range(1, NX):
SDIFF[rr, rr + 1] = mt.sqrt((rr + 1) * 0.5)
SDIFF[rr, rr - 1] = -mt.sqrt(rr * 0.5)
# Hermite function spectral transform in matrix form
STR_H = (HT[:, tdex].T).dot(W)
# Hermite function spatial derivative based on spectral differentiation
temp = (HTD[:, tdex]).dot(SDIFF[np.ix_(tdex, tdex)])
temp = temp.dot(STR_H)
DDMT = b * temp
# Output the full interpolation matrix
STR_H = (HT.T).dot(W)
# Hermite function spatial derivative based on spectral differentiation
temp = HTD.dot(SDIFF)
temp = temp.dot(STR_H)
DDMF = b * temp
return DDMF, DDMT, STR_H
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