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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
5/2010

Hierarchical Quadrature for Multidimensional Singular Integrals

Peter Meszmer

Abstract

We introduce a method for the evaluation of singular integrals arising in the discretisation of integral equations. The method is based on the idea of repeated subdivision of domains. The integrals defined on these subdomains are classified. Each class can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the relations between the classes. Therefore the approximate value of the singular integral only depends on the accuracy of the calculation of regular integrals.

Received:
Feb 4, 2010
Published:
Feb 4, 2010
MSC Codes:
65D32, 42B20
Keywords:
numerical cubature, singular integrals

Related publications

inJournal
2010 Repository Open Access
Peter Meszmer

Hierarchical quadrature for multidimensional singular integrals

In: Journal of numerical mathematics, 18 (2010) 2, pp. 91-117