Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles. An adaptive algorithm for computing an approximation to the integral of each element in a vector function f(x,y) over a two-dimensional region made up of triangles is presented. A FORTRAN implementation of the algorithm is included. The basic cubature rule used over each triangle is a 37-point symmetric rule of degree 13. Based on the same evaluation points the local error for each element in the approximation vector and for each triangle is computed using a sequence of null rule evaluations. A sophisticated error-estimation procedure tries, in a cautious manner, to decide whether we have asymptotic behavior locally for each function. Different actions are taken depending on that decision, and the procedure takes advantage of the basic rule’s polynomial degree when computing the error estimate in the asymptotic case. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 12 articles , 2 standard articles )

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  1. Kronbichler, M.; Schoeder, S.; Müller, C.; Wall, W. A.: Comparison of implicit and explicit hybridizable discontinuous Galerkin methods for the acoustic wave equation (2016)
  2. Mousavi, S. E.; Pask, J. E.; Sukumar, N.: Efficient adaptive integration of functions with sharp gradients and cusps in (n)-dimensional parallelepipeds (2012)
  3. Li, Chong-Jun; Dagnino, Catterina: An adaptive numerical integration algorithm for polygons (2010)
  4. Sommariva, A.; Vianello, M.: Product Gauss cubature over polygons based on Green’s integration formula (2007)
  5. Cools, Ronald; Haegemans, Ann: Algorithm 824: CUBPACK: A package for automatic cubature; framework description (2003)
  6. Thall, Peter F.; Cheng, Su-Chun: Treatment comparisons based on two-dimensional safety and efficacy alternatives in oncology trials (1999)
  7. Espelid, Terje O.: Remark on Algorithm 706: DCUTRI -- an algorithm for adaptive cubature over a collection of triangles (1998)
  8. Klees, Roland: Numerical calculation of weakly singular surface integrals (1996)
  9. Cariño, Ricolindo; Robinson, Ian; De Doncker, Elise: Adaptive cubature over a collection of triangles using the (d)- transformation (1994)
  10. Espelid, Terje O.: On integrating vertex singularities using extrapolation (1994)
  11. Berntsen, J.; Cools, R.; Espelid, T. O.: Algorithm 720: An algorithm for adaptive cubature over a collection of 3-dimensional simplices (1993)
  12. Berntsen, Jarle; Espelid, Terje O.: Algorithm 706: DCUTRI: An algorithm for adaptive cubature over a collection of triangles (1992)