tetrahedron_felippa_rule

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

Licensing:

The computer code and data files described and made available on this web page are 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.

Related Data and Programs:

annulus_rule, a MATLAB code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2d.

cube_felippa_rule, a MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a cube in 3d.

disk_rule, a MATLAB code which computes quadrature rules over the interior of a disk in 2d.

pyramid_felippa_rule, a MATLAB code which returns felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3d.

pyramid_rule, a MATLAB code which computes a quadrature rule over the interior of the unit pyramid in 3d.

simplex_gm_rule, a MATLAB code which defines grundmann-moeller quadrature rules over the interior of a simplex in m dimensions.

square_felippa_rule, a MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

stroud, a MATLAB code which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2d, 3d and n-dimensions.

tetrahedron_felippa_rule_test

tetrahedron_keast_rule, a MATLAB code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3d.

tetrahedron_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of a tetrahedron in 3d.

tetrahedron_ncc_rule, a MATLAB code which defines newton-cotes closed quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron_nco_rule, a MATLAB code which defines newton-cotes open quadrature rules over the interior of a tetrahedron in 3d.

triangle_dunavant_rule, a MATLAB code which defines dunavant rules for quadrature over the interior of a triangle in 2d.

triangle_fekete_rule, a MATLAB code which defines fekete rules for interpolation or quadrature over the interior of a triangle in 2d.

triangle_lyness_rule, a MATLAB code which returns lyness-jespersen quadrature rules over the interior of a triangle in 2d.

triangle_ncc_rule, a MATLAB code which defines newton-cotes closed (ncc) quadrature rules over the interior of a triangle in 2d.

triangle_nco_rule, a MATLAB code which defines newton-cotes open (nco) quadrature rules over the interior of a triangle in 2d.

triangle_wandzura_rule, a MATLAB code which defines wandzura rules for quadrature over the interior of a triangle in 2d.

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;