pyramid_rule, a Fortran90 code which generates a conical product quadrature rule over the interior of the unit pyramid in 3D.
The quadrature rules generated are all examples of conical product rules, and involve a kind of direct product of the form:
Legendre rule in X * Legendre rule in Y * Jacobi rule in Zwhere the Jacobi rule includes a factor of (1-Z)^2.
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_rule legendre_order jacobi_order filenamewhere
The information on this web page is distributed under the MIT license.
pyramid_rule 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.
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).