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Boundary element collocation method for solving the exterior Neumann problem for Helmholtz's equation in three dimensions

  • We describe a boundary integral equation that solves the exterior Neumann problem for the Helmholtz equation in three dimensions. The unique solution is found by approximating a Fredholm integral equation of the second kind with the boundary element collocation method. We prove uperconvergence at the collocation points, distinguishing the cases of even and odd interpolation. Numerical examples demonstrate the performance of the method solving the integral equation and confirm the superconvergence.

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Author: Andreas Kleefeld, Tzu-Chu Lin
URL:http://etna.mcs.kent.edu/vol.39.2012/pp113-143.dir/pp113-143.pdf
ISSN:1068-9613
Title of the source (English):Electronic transactions on numerical analysis
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2012
Tag:Fredholm integral equation of the second kind, Helmholtz's equation, exterior Neumann problem, boundary element collocation method, superconvergence
Volume/Year:39
First Page:113
Last Page:143
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Numerische Mathematik und Wissenschaftliches Rechnen
Institution name at the time of publication:Fakultät für Mathematik, Naturwissenschaften und Informatik (eBTU) / LS Mathematik, insbesondere Numerische Mathematik und Wissenschaftliches Rechnen
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