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https://github.com/wassname/simpeg.git
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ehaber99
94 lines
3.8 KiB
Python
94 lines
3.8 KiB
Python
import numpy as np
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from scipy import sparse as sp
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from sputils import sdiag, speye, kron3, spzeros
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from utils import mkvc
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def getEdgeMassMatrix(sigma,mesh):
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"""Get anisotropic mass matrix"""
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n = array([size(mesh.h[0]),size(mesh.h[1]),size(mesh.h[2])])
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nx = prod(n + [1, 0, 0])
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ex = reshape(arange(0,nx),[n[0]+1,n[1],n[2]])
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ny = prod(n + [0, 1, 0])
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ey = reshape(arange(0,ny),[n[0],n[1]+1,n[2]])
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nz = prod(n + [0, 0, 1]);
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ez = reshape(arange(0,nz),[n[0],n[1],n[2]+1])
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i = arange(0,n[0]-1); j = arange(0,n[1]-1); k = arange(0,n[2]-1)
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# corner i,j,k
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Px1 = take(ex,[i,j,k]); Py1 = take(ey,[i,j,k]); Pz1 = take(ez,[i,j,k])
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# corner i+1,j,k
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Px2 = take(ex,[i,j,k]); Py2 = take(ey,[i+1,j,k]); Pz2 = take(ez,[i+1,j,k])
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# corner i,j+1,k
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Px3 = take(ex,[i,j+1,k]); Py3 = take(ey,[i,j,k]); Pz3 = take(ez,[i,j+1,k])
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# corner i+1,j+1,k
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Px4 = take(ex,[i,j+1,k]); Py4 = take(ey,[i+1,j,k]); Pz4 = take(ez,[i+1,j+1,k]);
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# corner i,j,k+1
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Px5 = take(ex,[i,j,k+1]); Py5 = take(ey,[i,j,k+1]); Pz5 = take(ez,[i,j,k])
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# corner i+1,j,k+1
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Px6 = take(ex,[i,j,k+1]); Py6 = take(ey,[i+1,j,k+1]); Pz6 = take(ez,[i+1,j,k])
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# corner i,j+1,k+1
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Px7 = take(ex,[i,j+1,k+1]); Py7 = take(ey,[i,j,k+1]); Pz7 = take(ez,[i,j+1,k])
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# corner i+1,j+1,k+1
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Px8 = take(ex,[i,j+1,k+1]); Py8 = take(ey,[i+1,j,k+1]); Pz8 = take(ez,[i+1,j+1,k])
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nx1 = size(Px1); ny1 = size(Py1); nz1 = size(Pz1)
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#sparse.coo_matrix((V,(I,J)),shape=(4,4))
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P1 = block_diag(( sparse.coo_matrix(arange(0,nx1),Px1(:), e(nx1), nx1,nx),
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sparse.coo_matrix(arange(0,ny1),Py1(:),e(ny1), ny1,ny),
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sparse.coo_matrix(arange(0,nz1),Pz1(:),e(nz1), nz1,nz)))
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nx2 = numel(Px2); ny2 = numel(Py2); nz2 = numel(Pz2);
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P2 = blkdiag( sparse(1:nx2,Px2(:), e(nx2), nx2,nx) , ...
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sparse(1:ny2,Py2(:),e(ny2), ny2,ny), ...
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sparse(1:nz2,Pz2(:),e(nz2), nz2,nz));
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nx3 = numel(Px3); ny3 = numel(Py3); nz3 = numel(Pz3);
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P3 = blkdiag( sparse(1:nx3,Px3(:), e(nx3), nx3,nx) , ...
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sparse(1:ny3,Py3(:),e(ny3), ny3,ny), ...
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sparse(1:nz3,Pz3(:),e(nz3), nz3,nz));
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nx4 = numel(Px4); ny4 = numel(Py4); nz4 = numel(Pz4);
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P4 = blkdiag( sparse(1:nx4,Px4(:), e(nx4), nx4,nx) , ...
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sparse(1:ny4,Py4(:), e(ny4), ny4,ny), ...
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sparse(1:nz4,Pz4(:), e(nz4), nz4,nz));
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nx5 = numel(Px5); ny5 = numel(Py5); nz5 = numel(Pz5);
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P5 = blkdiag( sparse(1:nx5,Px5(:), e(nx5), nx5,nx) , ...
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sparse(1:ny5,Py5(:), e(ny5), ny5,ny), ...
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sparse(1:nz5,Pz5(:), e(nz5), nz5,nz));
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nx6 = numel(Px6); ny6 = numel(Py6); nz6 = numel(Pz6);
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P6 = blkdiag( sparse(1:nx6,Px6(:), e(nx6), nx6,nx) , ...
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sparse(1:ny6,Py6(:), e(ny6), ny6,ny), ...
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sparse(1:nz6,Pz6(:), e(nz6), nz6,nz));
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nx7 = numel(Px7); ny7 = numel(Py7); nz7 = numel(Pz7);
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P7 = blkdiag( sparse(1:nx7,Px7(:), e(nx7), nx7,nx) , ...
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sparse(1:ny7,Py7(:), e(ny7), ny7,ny), ...
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sparse(1:nz7,Pz7(:), e(nz7), nz7,nz));
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nx8 = numel(Px8); ny8 = numel(Py8); nz8 = numel(Pz8);
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P8 = blkdiag( sparse(1:nx8,Px8(:), e(nx8), nx8,nx) , ...
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sparse(1:ny8,Py8(:), e(ny8), ny8,ny), ...
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sparse(1:nz8,Pz8(:), e(nz8), nz8,nz));
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V = sdiag(sqrt([v(:); v(:); v(:)]));
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# generate the conductivity
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S = [sdiag(sig(:,1)) , sdiag(sig(:,4)) , sdiag(sig(:,5)); ...
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sdiag(sig(:,4)) , sdiag(sig(:,2)) , sdiag(sig(:,6)); ...
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sdiag(sig(:,5)) , sdiag(sig(:,6)) , sdiag(sig(:,3))];
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# scale by the volume
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S = V*S*V;
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M = 1/8*(P1'*S*P1 + P2'*S*P2 + P3'*S*P3 + P4'*S*P4 + ...
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P5'*S*P5 + P6'*S*P6 + P7'*S*P7 + P8'*S*P8);
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