FELIPPA
Finite Element Quadrature Rules


FELIPPA is a FORTRAN90 library which generates the points and weights of a quadrature rule for a variety of 1D, 2D and 3D regions of interest for computations involving the finite element method (FEM).

Regions for which rules are available, with a count of Corners, Edges, and Faces, include:
NameAcronymC+E+F
Line segmentLine2+1+0
TriangleTrig3+3+1
QuadrilateralQuad4+4+1
TetrahedronTetr4+6+4
WedgeWedg6+9+5
PyramidPyra5+8+5
HexahedronHexa8+12+6

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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

Related Data and Programs:

DISK_RULE, a FORTRAN90 library which computes quadrature rules for the unit disk in 2D, that is, the interior of the circle of radius 1 and center (0,0).

PYRAMID_RULE, a FORTRAN90 program which computes a quadrature rule for a pyramid.

SIMPLEX_GM_RULE, a FORTRAN90 library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.

STROUD, a FORTRAN90 library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TETRAHEDRON_KEAST_RULE, a FORTRAN90 library which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

TETRAHEDRON_MONTE_CARLO, a FORTRAN90 program which uses the Monte Carlo method to estimate integrals over a tetrahedron.

TETRAHEDRON_NCC_RULE, a FORTRAN90 library which defines Newton-Cotes closed quadrature rules on a tetrahedron.

TETRAHEDRON_NCO_RULE, a FORTRAN90 library which defines Newton-Cotes open quadrature rules on a tetrahedron.

TRIANGLE_DUNAVANT_RULE, a FORTRAN90 library which defines Dunavant rules for quadrature on a triangle.

TRIANGLE_FEKETE, a FORTRAN90 library which defines Fekete rules for interpolation or quadrature on a triangle.

TRIANGLE_LYNESS_RULE, a FORTRAN90 library which returns Lyness-Jespersen quadrature rules for the triangle.

TRIANGLE_MONTE_CARLO, a FORTRAN90 program which uses the Monte Carlo method to estimate integrals over a triangle.

TRIANGLE_NCC_RULE, a FORTRAN90 library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a FORTRAN90 library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_WANDZURA_RULE, a FORTRAN90 library which defines Wandzura rules for quadrature on a triangle.

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:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 16 July 2009.