Hierarchical quadrature for multidimensional singular integrals – Part II

Hierarchical quadrature for multidimensional singular integrals – Part II Abstract In a previous part I, we introduced a method for the evaluation of singular integrals arising in the discretization of integral equations based on the repeated subdivision of domains. The integrals defined on these subdomains are classified such that a class of integrals can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the relations between the classes. Furthermore the approximate value of the singular integrals only depends on the accuracy of the calculation of regular integrals. Part I left a gap on certain parameter configurations on which the mentioned system of equations is irregular. This paper shall close this gap. To this end, we introduce an alternative splitting strategy based on a modified Hadamard partie finie integral. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Numerical Mathematics de Gruyter

Hierarchical quadrature for multidimensional singular integrals – Part II

Journal of Numerical Mathematics, Volume 22 (1) – Mar 1, 2014

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
1570-2820
eISSN
1569-3953
DOI
10.1515/jnum-2014-0002
Publisher site
See Article on Publisher Site

Abstract

Abstract In a previous part I, we introduced a method for the evaluation of singular integrals arising in the discretization of integral equations based on the repeated subdivision of domains. The integrals defined on these subdomains are classified such that a class of integrals can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the relations between the classes. Furthermore the approximate value of the singular integrals only depends on the accuracy of the calculation of regular integrals. Part I left a gap on certain parameter configurations on which the mentioned system of equations is irregular. This paper shall close this gap. To this end, we introduce an alternative splitting strategy based on a modified Hadamard partie finie integral.

Journal

Journal of Numerical Mathematicsde Gruyter

Published: Mar 1, 2014

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