n-dimensional simplex quadrature

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

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)

[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.

[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

[Im Serious]

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

[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!