tetrahedron_felippa_rule

tetrahedron_felippa_rule, a Python 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 and an Octave version and a Python version.

Related Data and Programs:

simplex_gm_rule, a Python code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in m dimensions.

tetrahedron_grid, a Python code which computes a grid of points over the interior of a tetrahedron in 3D.

tetrahedron_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

tetrahedron_jaskowiec_rule, a Python 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.

tetrahedron_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of a tetrahedron 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:

• tetrahedron_felippa_rule.py, calls all the tests.
• tetrahedron_felippa_rule.sh, runs all the tests.
• tetrahedron_felippa_rule.txt, the output file.