PYRAMID_RULE\ Generate a Quadrature Rule for a Pyramid {#pyramid_rule-generate-a-quadrature-rule-for-a-pyramid align=”center”} ========================================
PYRAMID_RULE is 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 Z
where 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 GNU LGPL license.
PYRAMID_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
CUBE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
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.
PYRAMID_GRID, a C++ library which computes a grid of points over the interior of the unit pyramid in 3D;
PYRAMID_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
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.
SQUARE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a C++ library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.
TETRAHEDRON_FELIPPA_RULE, a C++ library which returns Felippa’s quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TRIANGLE_FEKETE_RULE, a C++ library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a C++ library which returns Felippa’s quadratures rules for approximating integrals over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a C++ library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.
You can go up one level to the C++ source codes.
Last revised on 23 July 2009.