TOMS706
(DCUTRI) - Quadrature over a Triangulated Region

TOMS706 is a FORTRAN77 library which approximates the integral of a function over a triangulated region.

Languages:

TOMS706 is available in a FORTRAN77 version.

Related Data and Programs:

DUNAVANT, a FORTRAN90 library which defines a Dunavant rule for quadrature over a triangle.

FEKETE, a FORTRAN90 library which defines a Fekete rule for quadrature or interpolation over a triangle.

MACHINE, a FORTRAN77 library which stores the appropriate values of machine constants for a given machine.

STROUD, a FORTRAN90 library which defines quadrature rules on a regions of a variety of shapes and dimensions.

TEST_TRI_INT, a FORTRAN90 library which can be used to test algorithms for quadrature over a triangle.

TOMS612, a FORTRAN77 library which estimates the integral of a function over a triangle.

TRIANGULATION, a FORTRAN90 library which carries out triangulations and includes some quadrature rules on triangles.

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

Reference:

1. Jarle Berntsen, Terje Espelid,
   Algorithm 706: DCUTRI, an Algorithm for Adaptive Cubature over a Collection of Triangles,
   ACM Transactions on Mathematical Software,
   Volume 18, Number 3, September 1992, pages 329-342.

Source Code:

• toms706.f, the source code.
• toms706.sh, commands to compile the source code.

Examples and Tests:

TOMS706_PRB1 is a simple example which integrates exp(x^2+y^2) over a single triangle.

• toms706_prb1.f, a sample calling program.
• toms706_prb1.sh, commands to compile and run the sample program.
• toms706_prb1_output.txt, the output from a run of the sample program.
• toms706_prb1_sun_output.txt, the expected output from the run.

TOMS706_PRB2 is an example which integrates many functions over a triangulated region.

• toms706_prb2.f, a sample calling program.
• toms706_prb2.sh, commands to compile and run the sample program.
• toms706_prb2_output.txt, the output from a run of the sample program.
• toms706_prb2_sun_output.txt, the expected output from the run.

List of Routines:

• D1MACH returns double precision machine-dependent constants.
• DCHTRI checks the validity of the input parameters to DCUTRI.
• DCUTRI integrates a function over a triangulated region.
• DRLTRI computes basic integration rules and error estimates.
• DTRTRI maintains a heap of subregions.
• DADTRI computes integrals over triangular regions.

You can go up one level to the FORTRAN77 source codes.