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n-dimensional simplex quadrature

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n-dimensional simplex quadrature

by Greg von Winckel

 

22 Dec 2005 (Updated 27 Dec 2005)

% Construct Gauss points and weights for a n-dimensional simplex

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Description

This script computes the weights and nodes for a Gauss quadrature rule on an n-dimensional simplex. The user can either specify the vertices of the simplex or only the dimension and the vertices of the unit simplex will then be used.

The first four simplexes are

n | Domain
--|------------
1 | Interval
2 | Triangle
3 | Tetrahedron
4 | Pentatope

Thanks to John D'Errico for helping with this script.

Acknowledgements
This submission has inspired the following:
Homogen Integrate on Triangular Area and Tetrahedral Volume
MATLAB release MATLAB 7 (R14)
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Comments and Ratings (4)
27 Dec 2005 John D'Errico

I've tested this code for simplexes in dimensions from 1
to 7. All results were correct in all tests. In 1-d of course,
its a 1-d Gauss-Legendre quadrature, easily verified from
tables. In higher dimensions all I could do was verify a
known result.
Its a nice piece of code, easy to use for an integration
over an entire simplicial complex.

20 Oct 2006 Chensong Zhang

Have not try it with my own applications. But it is very nice to have a small piece of code like this. Good Job

04 Mar 2008 Im Serious

This does integrate correctly. Was unable to debug the triangle quadrature function. Something to do with incorrect Y values.

03 Feb 2011 Herwig Peters

I use it for finite element coding, it works very well. I've checked it against other codes, very good agreement. Will stick with this one!

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Tag Activity for this File
Tag Applied By Date/Time
integration Greg von Winckel 22 Oct 2008 08:10:34
guass quadature Greg von Winckel 22 Oct 2008 08:10:34
simplex Greg von Winckel 22 Oct 2008 08:10:34
interval Greg von Winckel 22 Oct 2008 08:10:34
triangle Greg von Winckel 22 Oct 2008 08:10:34
tetrahedron Greg von Winckel 22 Oct 2008 08:10:34
pentatope Greg von Winckel 22 Oct 2008 08:10:34

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