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| HAL: hal-00310462, version 2 |
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| Computer Modeling in Engineering and Sciences 58 (2010) 271-296 |
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| Available versions: | v1 (2008-08-09) | v2 (2010-04-16) |
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| On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber |
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| A. Frangi 1Marc Bonnet 2 |
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| (2010) |
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| This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form $k=(\alpha+\rmi\beta)\vartheta$, 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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| 1: | Dipartimento di Ingegneria Strutturale |
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Politecnico di Milano |
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| 2: | Laboratoire de mécanique des solides (LMS) |
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CNRS : UMR7649 – Polytechnique - X – Mines ParisTech |
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| Subject | : | Physics/Mechanics/Mechanics of the solides Engineering Sciences/Mechanics/Mechanics of the solides |
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| Fast Multipole Method – Helmholtz problem – Complex wavenumber – Gegenbauer addition theorem |
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| hal-00310462, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00310462 | |
| oai:hal.archives-ouvertes.fr:hal-00310462 | |
| From: Marc Bonnet | |
| Submitted on: Friday, 16 April 2010 09:51:39 | |
| Updated on: Tuesday, 25 May 2010 14:22:28 | |
