tetrahedron_felippa_rule

tetrahedron_felippa_rule, a MATLAB code which generates Felippa quadrature rules over the interior of a tetrahedron in 3D.

Licensing:

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

Languages:

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

Related Data and Programs:

tetrahedron_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.
• subcomp_next.m, computes the next subcomposition of N into K parts.
• tetrahedron_unit_monomial.m, returns the exact integral of a monomial in a unit tetrahedron;
• tetrahedron_unit_o01.m, returns a 1 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o04.m, returns a 4 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o08.m, returns an 8 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o08b.m, returns an 8 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o14.m, returns a 14 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o14b.m, returns a 14 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o15.m, returns a 15 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o15.m, returns a 15 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o24.m, returns a 24 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_volume.m, computes the volume of the unit tetrahedron;