wedge_felippa_rule

wedge_felippa_rule, an Octave code which generates Felippa quadrature rules to estimate integrals over the interior of the unit wedge in 3D.

The interior of the unit wedge in 3D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
       -1 <= Z <= +1
      

Licensing:

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

Languages:

wedge_felippa_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:

wedge_felippa_rule_test

octave_rule, an Octave 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. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Source Code:

• comp_next.m, computes the compositions of the integer N into K parts.
• line_o01.m, returns a 1 point quadrature rule for the unit line.
• line_o02.m, returns a 2 point quadrature rule for the unit line.
• line_o03.m, returns a 3 point quadrature rule for the unit line.
• line_o04.m, returns a 4 point quadrature rule for the unit line.
• line_o05.m, returns a 5 point quadrature rule for the unit line.
• monomial_value.m, evaluates a monomial.
• subcomp_next.m, computes the next subcomposition of N into K parts.
• triangle_o01.m, returns a 1 point quadrature rule for the unit triangle.
• triangle_o03.m, returns a 3 point quadrature rule for the unit triangle.
• triangle_o03b.m, returns a 3 point quadrature rule for the unit triangle.
• triangle_o06.m, returns a 6 point quadrature rule for the unit triangle.
• triangle_o06b.m, returns a 6 point quadrature rule for the unit triangle.
• triangle_o07.m, returns a 7 point quadrature rule for the unit triangle.
• triangle_o12.m, returns a 12 point quadrature rule for the unit triangle.
• wedge_integral.m, returns the exact integral of a monomial in a unit wedge;
• wedge_rule.m, returns a quadrature rule for the unit wedge;
• wedge_volume.m, returns the volume of a unit wedge;