TY  - EJOU
AU  - Frangi, A.  
AU  - Bonnet, M.  

TI  - On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2010
VL  - 58
IS  - 3
SN  - 1526-1506

AB  - 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 <i>N</i> 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 <i>N</i> 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 <i>N</i> in terms of β.
KW  - Fast Multipole Method
KW  -  Helmholtz problem
KW  -  complex wavenumber
KW  -  Gegenbauer addition theorem

DO  - 10.3970/cmes.2010.058.271