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Gauss Quadrature for Tetrahedra

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16 Dec 2005 (Updated )

Compute Gauss weights and nodes for a specied tetrahedron

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Description

This script computes the (x,y,z) Gauss quadrature nodes and weights for a tetrahedron with user-specied vertices.

Acknowledgements

This file inspired Homogen Integrate On Triangular Area And Tetrahedral Volume.

MATLAB release MATLAB 7 (R14)
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Comments and Ratings (4)
27 Feb 2013 yj2011

Work wonderfully. One question. Not quite understand the Gauss Quadrature, but I noticed that the code by default outputs 64 note points. Can I increase the number of note points in order to improve the integration results?

19 Mar 2012 saurabh gupta  
21 Dec 2005 John D'Errico

Its fixed. Thanks Greg.

20 Dec 2005 John D'Errico

Wait until Greg fixes this. The following code fragment should compute the volume of a simple tetrahedron.
At the very least, since the function is constant over the
simplex domain, its integral should be positive.

V = [0 0 0;0 0 1;0 1 0;1 0 0];
[X,Y,Z,W]=tetraquad(4,V);
F = ones(size(X));
Q = W'*F

Q =
-0.1667

The magnitude is correct, just the sign is wrong. Q should be 1/6.

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