Hierarchical Quadrature for Multidimensional Singular Integrals

Peter Meszmer

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Submission date: 04. Feb. 2010 (revised version: July 2010)
Pages: 27
published in: Journal of numerical mathematics, 18 (2010) 2, p. 91-117 
DOI number (of the published article): 10.1515/JNUM.2010.004
Bibtex
MSC-Numbers: 65D32, 42B20
Keywords and phrases: numerical cubature, singular integrals
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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.