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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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1569-3953
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Volume 18, Issue 2

Issues

Hierarchical quadrature for multidimensional singular integrals

P. Meszmer
  • *Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany. Email:
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Published Online: 2010-06-21 | DOI: https://doi.org/10.1515/jnum.2010.004

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.

Keywords:: numerical cubature; singular integrals

About the article

Received: 2010-02-02

Revised: 2010-04-19

Published Online: 2010-06-21

Published in Print: 2010-06-01


Citation Information: Journal of Numerical Mathematics, Volume 18, Issue 2, Pages 91–117, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum.2010.004.

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[1]
Jonas Ballani and Peter Meszmer
Computing and Visualization in Science, 2012, Volume 15, Number 2, Page 75

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