square_felippa_rule

square_felippa_rule, a MATLAB code which returns a Felippa quadrature rule over the interior of a square in 2D.

Actually, the word "square" is meant to designate any quadrature region defined by:

        A(1) <= X <= B(1)
        A(2) <= Y <= B(2)
      

Licensing:

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

Languages:

square_felippa_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

square_felippa_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. 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_unit_o01.m, returns a 1 point quadrature rule for the unit line.
• line_unit_o02.m, returns a 2 point quadrature rule for the unit line.
• line_unit_o03.m, returns a 3 point quadrature rule for the unit line.
• line_unit_o04.m, returns a 4 point quadrature rule for the unit line.
• line_unit_o05.m, returns a 5 point quadrature rule for the unit line.
• monomial_value.m, evaluates a monomial.
• square_monomial.m, returns the exact integral of a monomial in a square in 2D.
• square_monomial_test.m, tests SQUARE_MONOMIAL.
• square_quad_test.m, tests the quadrature rules for a square in 2D.
• square_rule.m, returns a quadrature rule for a square in 2D;
• square_volume.m, returns the volume of a square in 2D;
• r8vec_direct_product.m, creates a direct product of R8VEC's.
• r8vec_direct_product2.m, creates a direct product of R8VEC's.
• subcomp_next.m, computes the next subcomposition of N into K parts.