Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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:
Jun 20, 2003
Published:
Jun 20, 2003
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