mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 13:20:13 +08:00
Rowan Cockett
88 lines
3.8 KiB
Python
88 lines
3.8 KiB
Python
from scipy import sparse as sp
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from sputils import sdiag
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from utils import sub2ind, ndgrid, mkvc
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import numpy as np
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def getEdgeInnerProduct(mesh, sigma):
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m = np.array([mesh.nCx, mesh.nCy, mesh.nCz])
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nc = mesh.nC
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i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2]))
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iijjkk = ndgrid(i, j, k)
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ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
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def Pxxx(pos):
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ind1 = sub2ind(mesh.nEx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]])
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ind2 = sub2ind(mesh.nEy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nE[0]
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ind3 = sub2ind(mesh.nEz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nE[0] + mesh.nE[1]
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IND = np.r_[ind1, ind2, ind3].flatten()
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return sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nE))).tocsr()
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# node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1)
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# / /
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# / / |
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# edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k)
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# / / |
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# / / |
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# node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k)
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# | | |
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# | | node(i+1,j+1,k+1)
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# | | /
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# edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k)
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# | | /
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# | | /
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# | |/
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# node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k)
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# no | node | e1 | e2 | e3
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# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
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# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
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# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
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# 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
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# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
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# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k
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# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k
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# 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k
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P000 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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P100 = Pxxx([[0, 0, 0], [1, 0, 0], [1, 0, 0]])
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P010 = Pxxx([[0, 1, 0], [0, 0, 0], [0, 1, 0]])
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P110 = Pxxx([[0, 1, 0], [1, 0, 0], [1, 1, 0]])
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P001 = Pxxx([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
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P101 = Pxxx([[0, 0, 1], [1, 0, 1], [1, 0, 0]])
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P011 = Pxxx([[0, 1, 1], [0, 0, 1], [0, 1, 0]])
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P111 = Pxxx([[0, 1, 1], [1, 0, 1], [1, 1, 0]])
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if sigma.size == mesh.nC: # Isotropic!
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sigma = mkvc(sigma) # ensure it is a vector.
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Sigma = sdiag(np.r_[sigma, sigma, sigma])
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elif sigma.shape[1] == 3: # Diagonal tensor
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Sigma = sdiag(np.r_[sigma[:, 0], sigma[:, 1], sigma[:, 2]])
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elif sigma.shape[1] == 6: # Fully anisotropic
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row1 = sp.hstack((sdiag(sigma[:, 0]), sdiag(sigma[:, 3]), sdiag(sigma[:, 4])))
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row2 = sp.hstack((sdiag(sigma[:, 3]), sdiag(sigma[:, 1]), sdiag(sigma[:, 5])))
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row3 = sp.hstack((sdiag(sigma[:, 4]), sdiag(sigma[:, 5]), sdiag(sigma[:, 2])))
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Sigma = sp.vstack((row1, row2, row3))
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# Cell volume
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v = np.sqrt(mesh.vol)
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v3 = np.r_[v, v, v]
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V = sdiag(v3)*Sigma*sdiag(v3) # to keep symmetry
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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
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A = 0.125*A
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return A
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if __name__ == '__main__':
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from TensorMesh import TensorMesh
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h = [np.array([1, 2, 3, 4]), np.array([1, 2, 1, 4, 2]), np.array([1, 1, 4, 1])]
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mesh = TensorMesh(h)
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sigma = np.ones((mesh.nC, 6))
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A = getEdgeInnerProduct(mesh, sigma)
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