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

A. Frangi1, M. Bonnet2
Politecnico di Milano, Milan (Italy), attilio.frangi@polimi.it
LMS (UMR CNRS 7649), Ecole Polytechnique, Palaiseau (France), bonnet@lms.polytechnique.fr

Computer Modeling in Engineering & Sciences 2010, 58(3), 271-296. https://doi.org/10.3970/cmes.2010.058.271

Abstract

This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ)ϑ, with α = 0,±1 and β > 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 β ≥ 1 it is observed that the value of N is independent of β and of the size of the octree cells employed while, for β < 1, simple empirical formulas are proposed yielding the required N in terms of β.

Keywords

Fast Multipole Method, Helmholtz problem, complex wavenumber, Gegenbauer addition theorem

Cite This Article

Frangi, A., Bonnet, M. (2010). On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber. CMES-Computer Modeling in Engineering & Sciences, 58(3), 271–296.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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