Hierarchical quadrature for multidimensional singular integrals

Hierarchical quadrature for multidimensional singular integrals 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Numerical Mathematics de Gruyter

Hierarchical quadrature for multidimensional singular integrals

Journal of Numerical Mathematics, Volume 18 (2) – Jun 1, 2010

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Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1570-2820
eISSN
1569-3953
DOI
10.1515/JNUM.2010.004
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Journal of Numerical Mathematicsde Gruyter

Published: Jun 1, 2010

Keywords: numerical cubature; singular integrals

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