PYRAMID_RULE, a C++ program which generates a quadrature rule over the interior of a 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 filenamewhere
The computer code and data files described and made available on this web page are distributed under the GNU LGPL 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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PYRAMID_EXACTNESS, a C++ program which investigates the polynomial exactness of a quadrature rule over the interior of the unit pyramid in 3D.
PYRAMID_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
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PYRAMID_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
QUADRATURE_RULES_PYRAMID, a dataset directory which contains quadrature rules over the interior of the unit pyramid in 3D.
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