Preprint 71/2012

Hierarchical quadrature for multidimensional singular integrals - part II

Peter Meszmer

Contact the author: Please use for correspondence this email.
Submission date: 12. Dec. 2012
Pages: 28
published in: Journal of numerical mathematics, 22 (2014) 1, p. 33-60 
DOI number (of the published article): 10.1515/jnum-2014-0002
Bibtex
Keywords and phrases: numerical cubature, singular integrals
Download full preprint: PDF (251 kB)

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.

03.07.2017, 01:42