pyramid_exactness, a C++ code which measures the precision of a quadrature rule 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).
pyramid_exactness filename degree_maxwhere
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.
CUBE_EXACTNESS, a C++ code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.
HYPERCUBE_EXACTNESS, a C++ 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 C++ code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
PYRAMID_GRID, a C++ code which computes a grid of points over the interior of the unit pyramid in 3D;
PYRAMID_INTEGRALS, a C++ 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 C++ 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 C++ code which can compute a quadrature rule over the interior of the unit pyramid in 3D.
QUADRATURE_RULES_PYRAMID, a dataset directory which contains quadrature rules over the interior of the unit pyramid in 3D.
SPHERE_EXACTNESS, a C++ code which tests the monomial exactness of a quadrature rule on the surface of the unit sphere in 3D.
SQUARE_EXACTNESS, a C++ code which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a rectangle in 2D.
TETRAHEDRON_EXACTNESS, a C++ code which investigates the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
TRIANGLE_EXACTNESS, a C++ code which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.
WEDGE_EXACTNESS, a C++ code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.