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Transformation of hypersingular integrals and black-box cubature


Sauter, S; Lage, C (2001). Transformation of hypersingular integrals and black-box cubature. Mathematics of Computation, 70(233):223-250 (electronic).

Abstract

In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals. In the second step, these integrals are reformulated as improper integrals. We will show that these integrals can be treated by cubature methods for weakly singular integrals as they exist in the literature.

Abstract

In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals. In the second step, these integrals are reformulated as improper integrals. We will show that these integrals can be treated by cubature methods for weakly singular integrals as they exist in the literature.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Finite-part integrals, regularisation, numerical integration, boundary element methods
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:19 Feb 2018 22:02
Publisher:American Mathematical Society
ISSN:0025-5718
Additional Information:First published in [Mathematics of Computation] in [vol. 70 (2001), no. 233], published by the American Mathematical Society
OA Status:Green
Publisher DOI:https://doi.org/10.1090/S0025-5718-00-01261-8
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1803126
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0958.65123

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