pyramid_exactness, a Python code which measures the precision of a quadrature rule defined over the interior of a pyramid in 3D.
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 described and made available on this web page are distributed under the MIT license
pyramid_exactness is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave versionand a Python version.
cube_exactness, a Python code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3d.
hypercube_exactness, a Python code which measures the monomial exactness of an m-dimensional quadrature rule over the interior of the unit hypercube in m dimensions.
pyramid_felippa_rule, a Python code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3d.
pyramid_grid, a Python code which computes a grid of points over the interior of the unit pyramid in 3d;
pyramid_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.
pyramid_jaskowiec_rule, a Python 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.
pyramid_monte_carlo, a Python 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 Python code which computes a conical product quadrature rule over the interior of the unit pyramid in 3d.
pyramid_witherden_rule, a Python code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid in 3D.
sphere_exactness, a Python code which tests the polynomial exactness of a quadrature rule over the surface of the unit sphere in 3d.
square_exactness, a Python code which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a square (rectangle/quadrilateral) in 2d.
tetrahedron_exactness a Python code which investigates the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.
triangle_exactness, a Python code which investigates the monomial exactness quadrature rule over the interior of a triangle in 2d.
wedge_exactness, a Python code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3d.
PYRAMID_L3X3_J3 is a pyramid rule formed by a conical product of a 3x3 Legendre rule and an order 3 Jacobi rule.