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Preprint (Vorabdruck) zugänglich unter
A Fourier transform based scheme for the Helmholtz equation
URN: urn:nbn:de:bsz:291-scidok-44026
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4402/
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Dokument 1.pdf (287 KB)
Freie Schlagwörter (Englisch):
Dirichlet problem , single- and double-layer potential
Institut:
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer:
73
Sprache:
Englisch
Erstellungsjahr:
2002
Publikationsdatum:
02.12.2011
Kurzfassung auf Englisch:
A new scheme based on the Fourier transform for the three-dimensional Helmholtz equation is introduced. We consider the boundary integral formulation for the Dirichlet boundary value problem and use the collocation boundary element method for the discretisation of the problem. In order to solve the resulting linear systems, the identity of the Fourier transform with respect to the wave number is applied to the associated matrices. We deduce the analytical forms and some important properties of the transformed matrices. Finally, some numerical examples for the solution are presented and we compare these with results using standard techniques.
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