Hierarchical Quadrature of Singular Integrals

Steffen Börm and Wolfgang Hackbusch

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Submission date: 20. Jun. 2003 (revised version: April 2004)
Pages: 26
published in: Computing, 74 (2005) 2, p. 75-100 
DOI number (of the published article): 10.1007/s00607-004-0076-0
Bibtex
with the following different title: Hierarchical quadrature for singular integrals
MSC-Numbers: 65D32, 42B20
Keywords and phrases: numerical quadrature, singular integrals
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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 hierarchical 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.