Open Access

ARTICLE

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

A. Frangi¹, M. Bonnet²

1 Politecnico di Milano, Milan (Italy), attilio.frangi@polimi.it
2 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.

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Keywords

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