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simpeg/SimPEG/getInnerProducts.py
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from scipy import sparse as sp
from sputils import sdiag
from utils import sub2ind, ndgrid, mkvc
import numpy as np
def getFaceInnerProduct(mesh, mu):
m = np.array([mesh.nCx, mesh.nCy, mesh.nCz])
nc = mesh.nC
i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2]))
iijjkk = ndgrid(i, j, k)
ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
def Pxxx(pos):
ind1 = sub2ind(mesh.nFx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]])
ind2 = sub2ind(mesh.nFy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nF[0]
ind3 = sub2ind(mesh.nFz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nF[0] + mesh.nF[1]
IND = np.r_[ind1, ind2, ind3].flatten()
return sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nF))).tocsr()
# node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1)
# / /
# / / |
# edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k)
# / / |
# / / |
# node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k)
# | | |
# | | node(i+1,j+1,k+1)
# | | /
# edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k)
# | | /
# | | /
# | |/
# node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k)
# no | node | e1 | e2 | e3
# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
# 100 | i+1,j ,k | i+1 ,j ,k | i,j ,k | i,j ,k
# 010 | i ,j+1,k | i ,j,k | i ,j+1 ,k | i ,j,k
# 110 | i+1,j+1,k | i+1 ,j,k | i,j+1 ,k | i,j,k
# 001 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k+1
# 101 | i+1,j ,k | i+1 ,j ,k | i,j ,k | i,j ,k+1
# 011 | i ,j+1,k | i ,j,k | i ,j+1 ,k | i ,j,k+1
# 111 | i+1,j+1,k | i+1 ,j,k | i,j+1 ,k | i,j,k+1
P000 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
P100 = Pxxx([[1, 0, 0], [0, 0, 0], [0, 0, 0]])
P010 = Pxxx([[0, 0, 0], [0, 1, 0], [0, 0, 0]])
P110 = Pxxx([[1, 0, 0], [0, 1, 0], [0, 0, 0]])
P001 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 1]])
P101 = Pxxx([[1, 0, 0], [0, 0, 0], [0, 0, 1]])
P011 = Pxxx([[0, 0, 0], [0, 1, 0], [0, 0, 1]])
P111 = Pxxx([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
if mu.size == mesh.nC: # Isotropic!
mu = mkvc(mu) # ensure it is a vector.
mu = sdiag(np.r_[mu, mu, mu])
elif mu.shape[1] == 3: # Diagonal tensor
mu = sdiag(np.r_[mu[:, 0], mu[:, 1], mu[:, 2]])
elif mu.shape[1] == 6: # Fully anisotropic
row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 3]), sdiag(mu[:, 4])))
row2 = sp.hstack((sdiag(mu[:, 3]), sdiag(mu[:, 1]), sdiag(mu[:, 5])))
row3 = sp.hstack((sdiag(mu[:, 4]), sdiag(mu[:, 5]), sdiag(mu[:, 2])))
mu = sp.vstack((row1, row2, row3))
# Cell volume
v = np.sqrt(mesh.vol)
v3 = np.r_[v, v, v]
V = sdiag(v3)*mu*sdiag(v3) # to keep symmetry
A = P000.T*V*P000 + P001.T*V*P001 + P010.T*V*P010 + P011.T*V*P011 + P100.T*V*P100 + P101.T*V*P101 + P110.T*V*P110 + P111.T*V*P111
A = 0.125*A
return A
def getEdgeInnerProduct(mesh, sigma):
m = np.array([mesh.nCx, mesh.nCy, mesh.nCz])
nc = mesh.nC
i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2]))
iijjkk = ndgrid(i, j, k)
ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
def Pxxx(pos):
ind1 = sub2ind(mesh.nEx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]])
ind2 = sub2ind(mesh.nEy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nE[0]
ind3 = sub2ind(mesh.nEz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nE[0] + mesh.nE[1]
IND = np.r_[ind1, ind2, ind3].flatten()
return sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nE))).tocsr()
# node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1)
# / /
# / / |
# edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k)
# / / |
# / / |
# node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k)
# | | |
# | | node(i+1,j+1,k+1)
# | | /
# edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k)
# | | /
# | | /
# | |/
# node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k)
# no | node | e1 | e2 | e3
# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
# 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k
# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k
# 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k
P000 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
P100 = Pxxx([[0, 0, 0], [1, 0, 0], [1, 0, 0]])
P010 = Pxxx([[0, 1, 0], [0, 0, 0], [0, 1, 0]])
P110 = Pxxx([[0, 1, 0], [1, 0, 0], [1, 1, 0]])
P001 = Pxxx([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
P101 = Pxxx([[0, 0, 1], [1, 0, 1], [1, 0, 0]])
P011 = Pxxx([[0, 1, 1], [0, 0, 1], [0, 1, 0]])
P111 = Pxxx([[0, 1, 1], [1, 0, 1], [1, 1, 0]])
if sigma.size == mesh.nC: # Isotropic!
sigma = mkvc(sigma) # ensure it is a vector.
Sigma = sdiag(np.r_[sigma, sigma, sigma])
elif sigma.shape[1] == 3: # Diagonal tensor
Sigma = sdiag(np.r_[sigma[:, 0], sigma[:, 1], sigma[:, 2]])
elif sigma.shape[1] == 6: # Fully anisotropic
row1 = sp.hstack((sdiag(sigma[:, 0]), sdiag(sigma[:, 3]), sdiag(sigma[:, 4])))
row2 = sp.hstack((sdiag(sigma[:, 3]), sdiag(sigma[:, 1]), sdiag(sigma[:, 5])))
row3 = sp.hstack((sdiag(sigma[:, 4]), sdiag(sigma[:, 5]), sdiag(sigma[:, 2])))
Sigma = sp.vstack((row1, row2, row3))
# Cell volume
v = np.sqrt(mesh.vol)
v3 = np.r_[v, v, v]
V = sdiag(v3)*Sigma*sdiag(v3) # to keep symmetry
A = P000.T*V*P000 + P001.T*V*P001 + P010.T*V*P010 + P011.T*V*P011 + P100.T*V*P100 + P101.T*V*P101 + P110.T*V*P110 + P111.T*V*P111
A = 0.125*A
return A
if __name__ == '__main__':
from TensorMesh import TensorMesh
h = [np.array([1, 2, 3, 4]), np.array([1, 2, 1, 4, 2]), np.array([1, 1, 4, 1])]
mesh = TensorMesh(h)
mu = np.ones((mesh.nC, 6))
A = getFaceInnerProduct(mesh, mu)
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