pyramid_jaskowiec_rule

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.
       

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

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.

Related Data and Programs:

pyramid_jaskowiec_rule_test

matlab_rule, a MATLAB 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).

Reference:

1. Jan Jaskowiec, Natarajan Sukumar,
   High order cubature rules for tetrahedra and pyramids,
   International Journal of Numerical Methods in Engineering,
   Volume 121, Number 11, pages 2418-2436, 15 June 2020.

Source Code:

• comp_next.m, returns the next composition of an integer.
• monomial_value.m, evaluates a multidimensional monomial.
• pyramid_jaskowiec_rule.m, returns a quadrature rule of given precision for the unit pyramid.
• pyramid_unit_monomial_integral.m, returns the exact integral of a given monomial over the unit pyramid.
• pyramid_unit_volume.m, returns the volume of the unit pyramid.
• pyramid_volume.m, returns the volume of a pyramid.
• rule_order.m, returns the number of quadrature points used in a rule of given degree.
• rule00.m, returns the rule of degree 0.
• rule01.m, returns the rule of degree 1.
• rule02.m, returns the rule of degree 2.
• rule03.m, returns the rule of degree 3.
• rule04.m, returns the rule of degree 4.
• rule05.m, returns the rule of degree 5.
• rule06.m, returns the rule of degree 6.
• rule07.m, returns the rule of degree 7.
• rule08.m, returns the rule of degree 8.
• rule09.m, returns the rule of degree 9.
• rule10.m, returns the rule of degree 10.
• rule11.m, returns the rule of degree 11.
• rule12.m, returns the rule of degree 12.
• rule13.m, returns the rule of degree 13.
• rule14.m, returns the rule of degree 14.
• rule15.m, returns the rule of degree 15.
• rule16.m, returns the rule of degree 16.
• rule17.m, returns the rule of degree 17.
• rule18.m, returns the rule of degree 18.
• rule19.m, returns the rule of degree 19.
• rule20.m, returns the rule of degree 20.

• pyramid_jaskowiec_rule_to_matlab.m, a MATLAB code which reads a data file describing one of the rules (with 128 digits) and writes a function to return points and weights.