pyramid_jaskowiec_rule, a MATLAB code which returns quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.
The integration region is:
- ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
When Z is zero, the integration region is a square lying in the (X,Y)
plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the
radius of the square diminishes, and when Z reaches 1, the square has
contracted to the single point (0,0,1).
The computer code and data files made available on this web page are distributed under the MIT license
pyramid_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.
hexagon_stroud_rule, a MATLAB code which computes one of four Stroud quadrature rules over the interior of the unit hexagon.
pyramid_exactness, a MATLAB code which investigates the polynomial exactness of a quadrature rule over the interior of the unit pyramid in 3d.
pyramid_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3d.
pyramid_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.
pyramid_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;
pyramid_rule, a MATLAB code which can compute a quadrature rule over the interior of the unit pyramid in 3d.
pyramid_witherden_rule, a MATLAB code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid in 3D.
quadrature_rules_pyramid, a dataset directory which contains quadrature rules over the interior of the unit pyramid in 3d.