# cube_felippa_rule

cube_felippa_rule, a MATLAB code which generates the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

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

```        A(1) <= X <= B(1)
A(2) <= Y <= B(2)
A(3) <= Z <= B(3)
```

### Languages:

cube_felippa_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

### Related Data and Programs:

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triangle_nco_rule, a matlab code which defines newton-cotes open (nco) quadrature rules over the interior of a triangle in 2d.

triangle_symq_rule, a matlab code which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2d, by hong xiao and zydrunas gimbutas.

triangle_wandzura_rule, a matlab code which defines wandzura rules for quadrature over the interior of a triangle in 2d.

wedge_felippa_rule, a matlab code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.

### 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:

Last revised on 22 December 2018.