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Universal quadratures for boundary integral equations on two-dimensional domains with corners

✍ Scribed by James Bremer; Vladimir Rokhlin; Ian Sammis

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 741 KB
Volume: 229
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2010.06.040

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✦ Synopsis

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace's equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.

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