24 lines
514 B
Mathematica
24 lines
514 B
Mathematica
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function [A,xy] = grid9(k)
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% GRID9 : Generate 9-point finite difference mesh.
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%
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% [A,xy] = GRID9(k) returns a k^2-by-k^2 symmetric positive definite
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% matrix A with the structure of the k-by-k 9-point grid,
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% and an array xy of coordinates for the grid points.
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a = blockdiags ([-4 20 -4], -1:1, k, k);
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b = blockdiags ([-1 -4 -1], -1:1, k, k);
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A = blockdiags ([b a b], -1:1, k, k);
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A = diag(diag(A)) - A;
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xy = zeros(k^2,2);
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x = ones(k,1) * (1:k);
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y = x';
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xy(:,1) = x(:);
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xy(:,2) = y(:);
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end
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