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Transformation of hypersingular integrals and black-box cubature


Authors: S. A. Sauter and C. Lage
Journal: Math. Comp. 70 (2001), 223-250
MSC (2000): Primary 65N38, 65R10, 65R20
DOI: https://doi.org/10.1090/S0025-5718-00-01261-8
Published electronically: June 12, 2000
MathSciNet review: 1803126
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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 Information

S. A. Sauter
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8050 Zürich, Switzerland
Email: stas@amath.unizh.ch

C. Lage
Affiliation: Coyote Systems, 2740 Van Ness Avenue #210, San Francisco, CA 94109
Email: lage@coyotesystems.com

DOI: https://doi.org/10.1090/S0025-5718-00-01261-8
Keywords: Finite-part integrals, regularisation, numerical integration, boundary element methods
Received by editor(s): January 8, 1998
Published electronically: June 12, 2000
Article copyright: © Copyright 2000 American Mathematical Society