TRIANGLE_FELIPPA_RULE
Felippa's Quadrature Rules for Triangles

TRIANGLE_FELIPPA_RULE is a FORTRAN77 library which generates the points and weights of Felippa's quadrature rules over the interior of a triangle in 2D.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TRIANGLE_FELIPPA_RULE is available in a C version and a C++ version and a FORTRAN90 version and a FORTRAN77 version and a MATLAB version.

Related Data and Programs:

CUBE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

PYRAMID_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

SQUARE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

TETRAHEDRON_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TRIANGLE_EXACTNESS, a FORTRAN77 program which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a FORTRAN77 program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_SVG, a FORTRAN77 library which uses Scalable Vector Graphics (SVG) to plot a triangle and any number of points, to illustrate quadrature rules and sampling techniques.

TRIANGLE_SYMQ_RULE, a FORTRAN77 library which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.

WEDGE_FELIPPA_RULE, a FORTRAN77 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

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:

• triangle_felippa_rule.f, the source code.
• triangle_felippa_rule.sh, BASH commands to compile the source code.

Examples and Tests:

• triangle_felippa_rule_prb.f, a sample calling program.
• triangle_felippa_rule_prb.sh, BASH commands to compile and run the sample program.
• triangle_felippa_rule_prb_output.txt, the output file.

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• MONOMIAL_VALUE evaluates a monomial.
• SUBCOMP_NEXT computes the next subcomposition of N into K parts.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_UNIT_MONOMIAL integrates a monomial over the unit triangle.
• TRIANGLE_UNIT_O01 returns a 1 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_O03 returns a 3 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_O03B returns a 3 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_O06 returns a 6 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_O06B returns a 6 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_O07 returns a 7 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_O12 returns a 12 point quadrature rule for the unit triangle.
• TRIANGLE_UNIT_VOLUME: volume of a unit triangle.

You can go up one level to the FORTRAN77 source codes.