mirror of
https://github.com/wassname/simpeg.git
synced 2026-07-10 05:55:26 +08:00
Rowan Cockett
182 lines
6.4 KiB
Python
182 lines
6.4 KiB
Python
from scipy.sparse import linalg
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from scipy import sparse
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from sputils import *
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from utils import *
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from numpy import *
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from TensorMesh import *
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# [A] = getEdgeInnerProduct(X,Y,Z,sigma)
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#
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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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def subarray(T, i1, i2, i3):
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return take(take(take(T, i1, 0), i2, 1), i3, 2)
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def getEdgeInnerProduct(mesh, sigma):
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h = mesh.h
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m = array([size(h[0]), size(h[1]), size(h[2])])
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nc = prod(m)
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me1 = m + array([0, 1, 1]); ne1 = prod(me1)
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me2 = m + array([1, 0, 1]); ne2 = prod(me2)
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me3 = m + array([1, 1, 0]); ne3 = prod(me3)
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i = int64(linspace(0,m[0]-1,m[0]))
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j = int64(linspace(0,m[1]-1,m[1]))
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k = int64(linspace(0,m[2]-1,m[2]))
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ii,jj,kk = ndgrid(i,j,k,vector=False)
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ii = mkvc(ii); jj = mkvc(jj); kk = mkvc(kk)
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## --------
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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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ind1 = sub2ind(me1,c_[ii,jj,kk])
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ind2 = sub2ind(me2,c_[ii,jj,kk]) + ne1
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ind3 = sub2ind(me3,c_[ii,jj,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P000 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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## --------
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# no | node | e1 | e2 | e3
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# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
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ind1 = sub2ind(me1,c_[ii,jj,kk])
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ind2 = sub2ind(me2,c_[ii+1,jj,kk]) + ne1
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ind3 = sub2ind(me3,c_[ii+1,jj,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P100 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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## --------
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# no | node | e1 | e2 | e3
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# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
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ind1 = sub2ind(me1,c_[ii,jj+1,kk])
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ind2 = sub2ind(me2,c_[ii,jj,kk]) + ne1
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ind3 = sub2ind(me3,c_[ii,jj+1,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P010 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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## --------
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# no | node | e1 | e2 | e3
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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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ind1 = sub2ind(me1,c_[ii,jj+1,kk])
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ind2 = sub2ind(me2,c_[ii+1,jj,kk]) + ne1
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ind3 = sub2ind(me3,c_[ii+1,jj+1,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P110 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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######
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## --------
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# no | node | e1 | e2 | e3
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# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
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ind1 = sub2ind(me1,c_[ii,jj,kk+1])
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ind2 = sub2ind(me2,c_[ii,jj,kk+1]) + ne1
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ind3 = sub2ind(me3,c_[ii,jj,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P001 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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## --------
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# no | node | e1 | e2 | e3
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# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k+1
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ind1 = sub2ind(me1,c_[ii,jj,kk+1])
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ind2 = sub2ind(me2,c_[ii+1,jj,kk+1]) + ne1
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ind3 = sub2ind(me3,c_[ii+1,jj,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P101 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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## --------
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# no | node | e1 | e2 | e3
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# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k+1
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ind1 = sub2ind(me1,c_[ii,jj+1,kk+1])
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ind2 = sub2ind(me2,c_[ii,jj,kk+1]) + ne1
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ind3 = sub2ind(me3,c_[ii,jj+1,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P011 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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## --------
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# no | node | e1 | e2 | e3
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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+1
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ind1 = sub2ind(me1,c_[ii,jj+1,kk+1])
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ind2 = sub2ind(me2,c_[ii+1,jj,kk+1]) + ne1
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ind3 = sub2ind(me3,c_[ii+1,jj+1,kk]) + ne1 + ne2
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IND = vstack((vstack((ind1,ind2)),ind3))
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IND = array(IND).flatten()
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P111 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr()
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# Cell volume
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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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v = sqrt(mesh.vol)
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v3 = r_[v, v, v]
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V = sdiag(v3)*Sigma*sdiag(v3)
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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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h = [array([1, 2, 3, 4]), array([1, 2, 1, 4, 2]), array([1, 1, 4, 1])]
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mesh = TensorMesh(h)
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sigma = ones((mesh.nC, 6))
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A = getEdgeInnerProduct(mesh, sigma)
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