5.0 | 3 ratings Rate this file 180 downloads (last 30 days) File Size: 2.18 KB File ID: #9435

n-dimensional simplex quadrature

22 Dec 2005 (Updated 27 Dec 2005)

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

File Information

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

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, Tessquad

MATLAB release

MATLAB 7 (R14)

Tags for This File
Everyone's Tags	guass quadature, integration, interval, pentatope, simplex, tetrahedron, triangle
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Comments and Ratings (3)
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.

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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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