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The exterior problem for the Helmholtz equation with mixed boundary conditions in three dimensions

  • In this article, a new integral equation is derived to solve the exterior problem for the Helmholtz equation with mixed boundary conditions in three dimensions, and existence and uniqueness is proven for all wave numbers. We apply the boundary element collocation method to solve the system of Fredholm integral equations of the second kind, where we use constant interpolation. We observe superconvergence at the collocation nodes and illustrate it with numerical results for several smooth surfaces.

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Metadaten
Author: Andreas Kleefeld
URL:http://www.tandfonline.com/doi/full/10.1080/00207160.2012.709932
DOI:https://doi.org/10.1080/00207160.2012.709932
ISSN:0020-7160
ISSN:1029-0265
Title of the source (English):International Journal of Computer Mathematics
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2012
Tag:Helmholtz equation, integral equation, mixed boundary conditions, boundary element collocation method, superconvergence
Volume/Year:89
Issue number:17
First Page:2392
Last Page:2409
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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