DECUHR: An algorithm for automatic integration of singular functions over a hyperrectangular region

DOI10.1007/BF02142691zbMath0811.65018OpenAlexW1974962751MaRDI QIDQ1344107

A. C. Genz, Terje O. Espelid

Publication date: 9 February 1995

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02142691

zbMATH Keywords

stabilitysingularityextrapolationsingular functionsFORTRAN implementationadaptive subdivision strategyautomatic cubature algorithm

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Software, source code, etc. for problems pertaining to measure and integration (28-04)

Related Items

Compliance and Hill polarization tensor of a crack in an anisotropic matrix ⋮ Adaptive numerical integration in element-free Galerkin methods for elliptic boundary value problems ⋮ Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method ⋮ Integrating composed singularities using nonuniform subdivision and extrapolation ⋮ The design and analysis of the generalized finite element method ⋮ Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems ⋮ Efficient integration of crack singularities in the extended finite element method: Duffy-distance transformation and conformal preconditioning strategy ⋮ An optimally convergent discontinuous Galerkin-based extended finite element method for fracture mechanics ⋮ DECUHR

Uses Software

• DCUHRE
• TRIEX

Cites Work

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• Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• On integrating vertex singularities using extrapolation
• An Error Functional Expansion for N-Dimensional Quadrature with an Integrand Function Singular at a Point
• An adaptive algorithm for the approximate calculation of multiple integrals
• Algorithm 698: DCUHRE
• Development of non-linear transformations for improving convergence of sequences