2013
DOI: 10.1016/j.jcp.2012.10.059
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Combining analytic preconditioner and Fast Multipole Method for the 3-D Helmholtz equation

Abstract: The paper presents a detailed numerical study of an iterative solution to 3-D sound-hard acoustic scattering problems at high frequency considering the Combined Field Integral Equation (CFIE). We propose a combination of an OSRC preconditioning technique and a Fast Multipole Method which leads to a fast and efficient algorithm independently of both a frequency increase and a mesh refinement. The OSRC-preconditioned CFIE exhibits very interesting spectral properties even for trapping domains. Moreover, this ana… Show more

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Cited by 52 publications
(87 citation statements)
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“…It has also been shown that different values of the coupling parameter can be chosen on different sections of the obstacle so long as its imaginary part is one-signed [33]; the ideas presented in this paper can equivalently be thought of as applying different values for the coupling parameter to different basis functions. [10,39]. The connection between these approaches and the Burton-Miller formulation is wellestablished, and it will be seen that the BIE proposed herein has strong similarities to some of them too.…”
Section: Non-uniquenessmentioning
confidence: 80%
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“…It has also been shown that different values of the coupling parameter can be chosen on different sections of the obstacle so long as its imaginary part is one-signed [33]; the ideas presented in this paper can equivalently be thought of as applying different values for the coupling parameter to different basis functions. [10,39]. The connection between these approaches and the Burton-Miller formulation is wellestablished, and it will be seen that the BIE proposed herein has strong similarities to some of them too.…”
Section: Non-uniquenessmentioning
confidence: 80%
“…This would however invalidate the energy argument made above for why normalisation of the basis functions makes sense, and it may also cause numerical problems since for on a planar boundary (we note that this issue also arises in the OSRC literature -see e.g. (12) of [39]). …”
Section: Normalisation Of Basis Functionsmentioning
confidence: 98%
“…They may however be derived and applied to other BIE formulations which are immune to fictitious eigenvalues such as that of Burton and Miller, see e.g. [27].…”
Section: Fast Bems For Frequency-domain Elastodynamicsmentioning
confidence: 99%
“…Now, expressing T C in terms of physical coordinates as the inverse partial Fourier transform (21) withÛ C replaced byT C and using polar coordinates in the Fourier space, one finally obtains (27) with the A ab (ξ) again as defined for (23).…”
Section: Multipole Expansions Of the Half-space Green's Tensormentioning
confidence: 99%
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