Show simple item record

dc.contributor.authorPareschi, Lorenzo
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorFilbet, Francis
dc.subjectBoltzmann equation ; Spectral methods ; Fast algorithms ; Entropyen
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.subject.ddclabelProbabilités et mathématiques appliquéesen

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record