KEAST
Quadrature Rules for a Tetrahedron

KEAST is a FORTRAN90 library, using double precision arithmetic, which defines a set of quadrature rules for the tetrahedron.

Licensing:

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

Related Data and Programs:

CUBPACK is a library of FORTRAN90 routines, using double precision arithmetic, which estimates the integral of a function (or vector of functions) over a collection of N-dimensional hyperrectangles and simplices.

DUNAVANT is a FORTRAN90 library of routines for defining Dunavant rules for quadrature on a triangle.

FEKETE is a FORTRAN90 library of routines for defining Fekete rules for quadrature or interpolation on a triangle.

FELIPPA is a MATHEMATICA library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.

GM_RULES is a FORTRAN90 library of routines for defining a Grundmann-Moeller rule for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.

KEAST is also available in a C++ version and a MATLAB version.

NCC_TETRAHEDRON is a FORTRAN90 library defining Newton-Cotes Closed quadrature rules on a tetrahedron.

NCO_TETRAHEDRON is a FORTRAN90 library defining Newton-Cotes Open quadrature rules on a tetrahedron.

NINT_EXACTNESS_TET is an executable FORTRAN90 program which investigates the polynomial exactness of a quadrature rule for the tetrahedron.

NINTLIB is a FORTRAN90 library containing a variety of routines for numerical estimation of integrals in multiple dimensions.

QUADRATURE_RULES_TET is a dataset directory of triples of files defining various quadrature rules on tetrahedrons.

QUADRULE is a FORTRAN90 library which includes a library of routines for defining quadrature rules on a variety of intervals with different weight functions.

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

WANDZURA is a FORTRAN90 library of routines for defining Wandzura rules for quadrature on a triangle.

Reference:

1. Patrick Keast,
   Moderate Degree Tetrahedral Quadrature Formulas,
   Computer Methods in Applied Mechanics and Engineering,
   Volume 55, Number 3, May 1986, pages 339-348.

Source Code:

• keast.f90, the source code.
• keast.csh, commands to compile the source code.

Examples and Tests:

• keast_prb.f90, a sample calling program.
• keast_prb.csh, commands to compile and run the sample program.
• keast_prb_output.txt, the output from a run of the sample program.

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• I4_MODP returns the nonnegative remainder of I4 division.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• KEAST_DEGREE returns the degree of a Keast rule for the tetrahedron.
• KEAST_ORDER_NUM returns the order of a Keast rule for the tetrahedron.
• KEAST_RULE returns the points and weights of a Keast rule.
• KEAST_RULE_NUM returns the number of Keast rules for the tetrahedron.
• KEAST_SUBORDER returns the suborders for a Keast rule.
• KEAST_SUBORDER_NUM returns the number of suborders for a Keast rule.
• KEAST_SUBRULE returns a compressed Keast rule.
• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_DET_4D computes the determinant of a 4 by 4 R8MAT.
• TETRAHEDRON_REFERENCE_TO_PHYSICAL maps T4 reference points to physical points.
• TETRAHEDRON_VOLUME computes the volume of a tetrahedron in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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