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.
Author: | Andreas Kleefeld |
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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 |