Geodesic
High order semi-lagrangian particle methods for transport equations: numerical analysis and implementation issues
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1029-1060

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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.

DOI : 10.1051/m2an/2014009
Classification : 65M12, 65M75, 65Y05, 65Y20
Keywords: advection equations, particle methods, semi-lagrangian methods, GPU computing 
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     author = {Cottet, G.-H. and Etancelin, J.-M. and Perignon, F. and Picard, C.},
     title = {High order semi-lagrangian particle methods for transport equations: numerical analysis and implementation issues},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1029--1060},
     publisher = {EDP-Sciences},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014009/}
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Cottet, G.-H.; Etancelin, J.-M.; Perignon, F.; Picard, C. High order semi-lagrangian particle methods for transport equations: numerical analysis and implementation issues. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1029-1060. doi: 10.1051/m2an/2014009

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