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, Volume 74, Issue 2, pp 75–100 | Cite as

Hierarchical Quadrature for Singular Integrals

  • S. BörmEmail author
  • W. Hackbusch
Article

Abstract

We introduce a method for the computation of singular integrals arising in the discretization of integral equations. The basic method is based on the concept of admissible subdomains, known, e.g., from panel clustering techniques and Open image in new window -matrices: We split the domain of integration into a hierarchy of subdomains and perform standard quadrature on those subdomains that are amenable to it. By using additional properties of the integrand, we can significantly reduce the algorithmic complexity of our approach. The method works also well for hypersingular integrals.

AMS Subject Classifications:

65D32 42B20 

Keywords

Numerical quadrature singular integrals 

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Copyright information

© Springer-Verlag Wien 2005

Authors and Affiliations

  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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