pyramid_felippa_rule

pyramid_felippa_rule, a MATLAB code which returns a Felippa quadrature rule over the interior of the unit pyramid in 3D.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

pyramid_felippa_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

pyramid_felippa_rule_test

matlab_rule, a MATLAB code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

1. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Source Code:

• comp_next.m, computes the compositions of the integer N into K parts.
• monomial_value.m, evaluates a monomial.
• pyra_unit_monomial.m, returns the exact integral of a monomial in a unit pyramid;
• pyra_unit_o01.m, returns a 1 point quadrature rule for the unit pyramid.
• pyra_unit_o05.m, returns a 5 point quadrature rule for the unit pyramid.
• pyra_unit_o06.m, returns a 6 point quadrature rule for the unit pyramid.
• pyra_unit_o08.m, returns an 8 point quadrature rule for the unit pyramid.
• pyra_unit_o08b.m, returns an 8 point quadrature rule for the unit pyramid.
• pyra_unit_o09.m, returns a 9 point quadrature rule for the unit pyramid.
• pyra_unit_o13.m, returns a 13 point quadrature rule for the unit pyramid.
• pyra_unit_o18.m, returns an 18 point quadrature rule for the unit pyramid.
• pyra_unit_o27.m, returns a 27 point quadrature rule for the unit pyramid.
• pyra_unit_o48.m, returns a 48 point quadrature rule for the unit pyramid.
• pyra_unit_volume.m, returns the volume of a unit pyramid;
• r8_mop.m, returns the I-th power of -1 as an R8.
• subcomp_next.m, computes the next subcomposition of N into K parts.