A high order fast multipole boundary element method

Publikationstyp
Conference Paper
Publikationsdatum
2015
Sprache
English
Author
Keuchel, Sören 
Vater, Kerstin orcid-logo
Estorff, Otto von 
Institut
Modellierung und Berechnung M-16 
TORE-URI
http://hdl.handle.net/11420/7844
Citation
22nd International Congress on Sound and Vibration, ICSV 2015: (2015)
Contribution to Conference
22nd International Congress on Sound and Vibration, ICSV 2015 
Scopus ID
2-s2.0-84971268643
The Boundary Element Method can be used to solve the Helmholtz equation in three dimensions. Just the surface has to be discretized, but a solution for the complete domain is obtained. Especially for exterior domains this is an enormous advantage. A drawback of the solution procedure, however is its quadratic complexity. The Fast Multipole Method results in a quasi linear complexity due to an approximation of a matrix vector product and is therefore applicable for solving large scale systems. The variables on the surface are approximated by ansatz functions of a certain order. Typically constant, linear or quadratic element orders are used. In this contribution formulations for arbitrary ansatz functions are presented. Since an application to exterior cases leads to the problem of fictitious frequencies, a Burton Miller formulation is embedded. The presented Collocation Method can treat the hypersingular kernels for arbitrary ansatz functions correctly. The theoretical background is introduced and numerical examples show the performance of the formulation.
DDC Class
600: Technik