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Article Dans Une Revue Computer Modeling in Engineering and Sciences Année : 2010

On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber

Résumé

This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form $k=(\alpha+\beta)\vartheta$, with $\alpha=0,\pm1$ and $\beta>0$, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a priori indication on the number $N$ of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For $\beta\geq 1$ it is observed that the value of $N$ is independent of $\beta$ and of the size of the octree cells employed while, for $\beta<1$, simple empirical formulas are proposed yielding the required $N$ in terms of $\beta$.
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Dates et versions

hal-00310462 , version 1 (09-08-2008)
hal-00310462 , version 2 (16-04-2010)

Identifiants

Citer

Attilio Frangi, Marc Bonnet. On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber. Computer Modeling in Engineering and Sciences, 2010, 58, pp.271-296. ⟨10.3970/cmes.2010.058.271⟩. ⟨hal-00310462v2⟩
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