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High order Semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues

Abstract : This paper is devoted to the definition, analysis and implementation of semi-Lagrangian methods as they result from particle methods combined with remeshing. We give a complete consistency analysis of these methods, based on the regularity and momentum properties of the remeshing kernels, and a stability analysis of a large class of second and fourth order methods. This analysis is supplemented by numerical illustrations. We also describe a general approach to implement these methods in the context of hybrid computing and investigate their performance on GPU processors as a function of their order of accuracy.
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https://hal.archives-ouvertes.fr/hal-00991150
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Submitted on : Wednesday, May 14, 2014 - 7:24:28 PM
Last modification on : Tuesday, October 19, 2021 - 11:13:16 PM
Long-term archiving on: : Thursday, August 14, 2014 - 12:10:11 PM

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Georges-Henri Cottet, Jean-Matthieu Etancelin, Franck Pérignon, Christophe Picard. High order Semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2014, 48 (4), pp.1029-1060. ⟨10.1051/m2an/2014009⟩. ⟨hal-00991150⟩

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