32 lines
704 B
Mathematica
32 lines
704 B
Mathematica
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function [A,xyz] = grid3d(k)
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% GRID3D : Generate 3-dimensional 7-point finite difference mesh.
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%
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% [A,xyz] = GRID3D(k) returns a k^3-by-k^3 symmetric positive definite
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% matrix A with the structure of the k-by-k-by-k 7-point grid,
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% and an array xyz of coordinates for the grid points.
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a = blockdiags ([-1 6 -1], -1:1, k, k);
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I = speye (k, k);
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aa = blockdiags ([-I a -I], -1:1, k, k);
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II = speye(k^2,k^2);
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A = blockdiags ([-II aa -II], -1:1, k, k);
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A = diag(diag(A)) - A;
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xyz = zeros(k^3,3);
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x = ones(k,1) * (1:k);
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y = x';
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j = 1;
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for i = 1:k
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xyz(j:j+k^2-1 , 1) = x(:);
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xyz(j:j+k^2-1 , 2) = y(:);
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xyz(j:j+k^2-1 , 3) = i * ones(k^2,1);
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j = j + k^2;
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end
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end
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