CUBPACK aims to offer a collection of re-usable code for automatic n-dimensional (n greater than or equal to 1) numerical integration of functions over a collection of regions, i.e., quadrature and cubature. The current version allows this region to consist of a union of n-simplices and n-parellellepids. The framework of CUBPACK is described as well as its user interface. The functionality of several well known routines is embedded. New features include integration algorithms using the epsilon-algorithm for extrapolation for regions other than triangles and the implementation of a new type of subdivision for 3-cubes.

References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Benvenuti, Elena; Ventura, Giulio; Ponara, Nicola; Tralli, Antonio: Accuracy of three-dimensional analysis of regularized singularities (2015)
  2. Benvenuti, Elena: XFEM with equivalent eigenstrain for matrix-inclusion interfaces (2014)
  3. Adler, Stephen L.: The guide to PAMIR. Theory and use of parameterized adaptive multidimensional integration routines (2013)
  4. Benvenuti, Elena; Ventura, Giulio; Ponara, Nicola; Tralli, Antonio: Variationally consistent eXtended FE model for 3D planar and curved imperfect interfaces (2013)
  5. Poppe, Koen; Cools, Ronald: CHEBINT, a MATLAB/Octave toolbox for fast multivariate integration and interpolation based on Chebyshev approximations over hypercubes (2013)
  6. Zhang, Qinghai: Highly accurate Lagrangian flux calculation via algebraic quadratures on spline-approximated donating regions (2013)
  7. Huybrechs, Daan; Olver, Sheehan: Superinterpolation in highly oscillatory quadrature (2012)
  8. Nuyens, Dirk; Waterhouse, Benjamin J.: A global adaptive quasi-Monte Carlo algorithm for functions of low truncation dimension applied to problems from finance (2012)
  9. Baldoni, Velleda; Berline, Nicole; De Loera, Jesús A.; Köppe, Matthias; Vergne, Michèle: How to integrate a polynomial over a simplex (2011)
  10. Santin, G.; Sommariva, A.; Vianello, M.: An algebraic cubature formula on curvilinear polygons (2011)
  11. Farrell, P.E.; Maddison, J.R.: Conservative interpolation between volume meshes by local Galerkin projection (2010)
  12. Li, Tiancheng; Robinson, Ian: Algorithm 906: elrint3d -- a three-dimensional nonadaptive automatic cubature routine using a sequence of embedded lattice rules (2010)
  13. Baveja, Manas; Wein, Lawrence M.: An effective two-finger, two-stage biometric strategy for the US-VISIT program (2009)
  14. Huybrechs, Daan; Cools, Ronald: On generalized Gaussian quadrature rules for singular and nearly singular integrals (2009)
  15. Huybrechs, Daan; Vandewalle, Stefan: An efficient implementation of boundary element methods for computationally expensive Green’s functions (2008)
  16. Huybrechs, Daan; Vandewalle, Stefan: A sparse discretization for integral equation formulations of high frequency scattering problems (2007)
  17. Cools, Ronald: Subdivision strategies in adaptive integration algorithms (2004)
  18. Cools, Ronald: Extrapolation and adaptivity in software for automatic numerical integration on a cube (2003)
  19. Cools, Ronald; Haegemans, Ann: Algorithm 824: CUBPACK: A package for automatic cubature; framework description (2003)
  20. Genz, Alan; Cools, Ronald: An adaptive numerical cubature algorithm for simplices (2003)

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