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MiS Preprint

Hierarchical Quadrature of Singular Integrals

Steffen Börm and Wolfgang Hackbusch


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.

MSC Codes:
65D32, 42B20
numerical quadrature, singular integrals

Related publications

2005 Repository Open Access
Steffen Börm and Wolfgang Hackbusch

Hierarchical quadrature for singular integrals

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