59 lines
1.4 KiB
Mathematica
59 lines
1.4 KiB
Mathematica
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function[quadrature]=GaussQuadrature(GaussOption)
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% Compute the Gauss Point with their weights
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% Case 1: Quad 1x1
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% Case 2: Quad 2x2
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% Case 3: Quad 3x3
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% Gauss points are automatically chosen relative to shape function
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quadrature=struct();
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switch GaussOption
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case 'gauss1'
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quadrature.points=[0 0];
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quadrature.weights=4;
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case 'gauss2'
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quadrature.points=[...
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-1/sqrt(3) -1/sqrt(3)
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1/sqrt(3) -1/sqrt(3)
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1/sqrt(3) 1/sqrt(3)
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-1/sqrt(3) 1/sqrt(3)];
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quadrature.weights=ones(size(quadrature.points,1),1);
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case 'gauss3'
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quadrature.points=[...
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0 0
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sqrt(3/5) sqrt(3/5)
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-sqrt(3/5) sqrt(3/5)
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-sqrt(3/5) -sqrt(3/5)
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sqrt(3/5) -sqrt(3/5)
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0 sqrt(3/5)
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-sqrt(3/5) 0
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0 -sqrt(3/5)
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sqrt(3/5) 0];
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quadrature.weights=[...
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64/81
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25/81
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25/81
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25/81
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25/81
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40/81
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40/81
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40/81
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40/81];
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end
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figure
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grid on, hold on
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scatter(quadrature.points(:,1),quadrature.points(:,2),'*');
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axis([-1 1 -1 1]);
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for i=1:size(quadrature.points,1)
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text(quadrature.points(i,1),quadrature.points(i,2)+0.1,num2str(i),'FontSize',14);
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end
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return
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