tetrahedron_jaskowiec_rule

tetrahedron_jaskowiec_rule, a Fortran90 code which returns quadrature rules, with exactness up to total degree 20, over the interior of a tetrahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.

The quadrature rules are described in terms of barycentric coordinates (a,b,c,d), with weights w that sum to 1.

Licensing:

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

Languages:

tetrahedron_jaskowiec_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:

tetrahedron_jaskowiec_rule_test

f90_rule, a Fortran90 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. Jan Jaskowiec, Natarajan Sukumar,
   High order cubature rules for tetrahedra and pyramids,
   International Journal of Numerical Methods in Engineering,
   Volume 121, Number 11, pages 2418-2436, 15 June 2020.
2. Jan Jaskowiec, Natarajan Sukumar,
   High order symmetric cubature rules for tetrahedra and pyramids,
   International Journal of Numerical Methods in Engineering,
   Volume 122, Number 1, pages 148-171, 24 August 2020.

Source Code:

• tetrahedron_jaskowiec_rule.f90, the source code.
• tetrahedron_jaskowiec_rule.sh, compiles the source code.

• tetrahedron_jaskowiec_rule_to_c.m, a MATLAB script which reads a data file describing one of the rules (with 128 digits) and writes a Fortran90 function to return points and weights.