pyramid_rule, a MATLAB code which generates a quadrature rule over the interior of the unit pyramid in 3D.
The quadrature rules generated by PYRAMID_RULE are all examples of conical product rules, and involve a kind of direct product of the form:
Legendre rule in X * Legendre rule in Y * Jacobi rule in Zwhere the Jacobi rule includes a factor of (1-Z)^2.
The integration region is:
- ( 1 - Z ) <= X <= 1 - Z - ( 1 - Z ) <= Y <= 1 - Z 0 <= Z <= 1.When Z is zero, the integration region is a square lying in the (X,Y) plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the radius of the square diminishes, and when Z reaches 1, the square has contracted to the single point (0,0,1).
pyramid_rule ( legendre_order, jacobi_order, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the MIT license
pyramid_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
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