Sauter, S A; Lage, C (2001). Transformation of hypersingular integrals and black-box cubature. Mathematics of Computation, 70(233):223-250 (electronic).
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Algebra and Number Theory
Physical Sciences > Computational Mathematics Physical Sciences > Applied 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: | 23 Jan 2022 14:40 |
| 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: | Hybrid |
| 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 |
Sauter, S A