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| HAL : hal-00661151, version 1 |
| arXiv : 1201.3986 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (19-01-2012) | v2 (14-12-2012) |
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| Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation |
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| Clément Mouhot 1Lorenzo Pareschi 2 |
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| (18/01/2012) |
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| Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the velocity space. In this paper, following the ideas introduced in [26,27], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from $O(N^{2d+1})$ to $O(\bar{N}^d N^d\log_2 N)$, $\bar{N} << N$, with almost no loss of accuracy. |
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| 1 : | DPMMS/CMS |
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University of Cambridge |
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| 2 : | Department of Mathematics (DPT OF MATH., UNIV. OF FERRARA) |
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Università degli studi di Ferrara |
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| 3 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Analyse numérique Mathématiques/Equations aux dérivées partielles |
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| Boltzmann equation – Discrete-velocity approximations – Discrete-Velocity Methods – Fast summation methods – Farey series – Convolutive decomposition |
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| hal-00661151, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00661151 | |
| oai:hal.archives-ouvertes.fr:hal-00661151 | |
| Contributeur : Clément Mouhot | |
| Soumis le : Mercredi 18 Janvier 2012, 16:24:29 | |
| Dernière modification le : Jeudi 19 Janvier 2012, 08:44:51 | |
