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MiS Preprint

Hierarchical Quadrature for Multidimensional Singular Integrals

Peter Meszmer


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.

MSC Codes:
65D32, 42B20
numerical cubature, singular integrals

Related publications

2010 Repository Open Access
Peter Meszmer

Hierarchical quadrature for multidimensional singular integrals

In: Journal of numerical mathematics, 18 (2010) 2, pp. 91-117