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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
50/2003

Hierarchical Quadrature of Singular Integrals

Steffen Börm and Wolfgang Hackbusch

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.

Received:
20.06.03
Published:
20.06.03
MSC Codes:
65D32, 42B20
Keywords:
numerical quadrature, singular integrals

Related publications

inJournal
2005 Repository Open Access
Steffen Börm and Wolfgang Hackbusch

Hierarchical quadrature for singular integrals

In: Computing, 74 (2005) 2, pp. 75-100