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Solving the Boltzmann equation in N log2 N

dc.contributor.authorPareschi, Lorenzo
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorFilbet, Francis
dc.date.accessioned2009-06-18T09:49:27Z
dc.date.available2009-06-18T09:49:27Z
dc.date.issued2006
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/338
dc.language.isoenen
dc.subjectBoltzmann equation ; Spectral methods ; Fast algorithms ; Entropyen
dc.subject.ddc519en
dc.titleSolving the Boltzmann equation in N log2 Nen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in dimension three. These algorithms are implemented for the solution of the Boltzmann equation in two and three dimension, first for homogeneous solutions, then for general non homogeneous solutions. The results are compared to explicit solutions, when available, and to Monte-Carlo methods. In particular, the computational cost and accuracy are compared to those of Monte-Carlo methods as well as to those of previous spectral methods. Finally, for inhomogeneous solutions, we take advantage of the great computational efficiency of the method to show an oscillation phenomenon of the entropy functional in the trend to equilibrium, which was suggested in the work [L. Desvillettes and C. Villani, Invent. Math., 159 (2005), pp. 245-316].en
dc.relation.isversionofjnlnameSIAM Journal on Scientific Computing
dc.relation.isversionofjnlvol28en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2006
dc.relation.isversionofjnlpages1029–1053en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/050625175en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00087321/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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