DECUHR: An algorithm for automatic integration of singular functions over a hyperrectangular region. We describe an automatic cubature algorithm for functions that have a singularity on the surface of the integration region. The algorithm combines an adaptive subdivision strategy with extrapolation. The extrapolation uses a non-uniform subdivision that can be directly incorporated into the subdivision strategy used for the adaptive algorithm. The algorithm is designed to integrate a vector function over an n-dimensional rectangular region and a FORTRAN implementation is included.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Poppe, Koen; Cools, Ronald: CHEBINT, a MATLAB/Octave toolbox for fast multivariate integration and interpolation based on Chebyshev approximations over hypercubes (2013)
  2. Mousavi, S. E.; Sukumar, N.: Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method (2010)
  3. Mousavi, S. E.; Sukumar, N.: Generalized Duffy transformation for integrating vertex singularities (2010)
  4. Shen, Yongxing; Lew, Adrian: An optimally convergent discontinuous Galerkin-based extended finite element method for fracture mechanics (2010)
  5. Barthélémy, Jean-François: Compliance and Hill polarization tensor of a crack in an anisotropic matrix (2009)
  6. Park, Kyoungsoo; Pereira, Jeronymo P.; Duarte, C. Armando; Paulino, Glaucio H.: Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems (2009)
  7. Simone, A.; Duarte, C. A.; Van Der Giessen, E.: A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries (2006)
  8. Xiao, Q. Z.; Karihaloo, B. L.: Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery (2006)
  9. Liu, X. Y.; Xiao, Q. Z.; Karihaloo, B. L.: XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials (2004)
  10. Binoth, T.; Heinrich, G.; Kauer, N.: A numerical evaluation of the scalar hexagon integral in the physical region (2003)
  11. Cools, Ronald: Extrapolation and adaptivity in software for automatic numerical integration on a cube (2003)
  12. Kauer, Nikolas: SINGINT: automatic numerical integration of singular integrands (2003)
  13. Strouboulis, T.; Babuška, I.; Copps, K.: The design and analysis of the generalized finite element method (2000)
  14. Singstad, Kristoffer; Espelid, Terje O.: Integrating composed singularities using nonuniform subdivision and extrapolation (1999)
  15. Espelid, Terje O.; Genz, Alan: DECUHR: An algorithm for automatic integration of singular functions over a hyperrectangular region (1994)