Volume 48, Number 4, July-August 2014
|Page(s)||1029 - 1060|
|Published online||30 June 2014|
High order semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues
UniversitéGrenoble Alpes and CNRS, Laboratoire Jean
Kuntzmann, BP 53
38041, Grenoble Cedex
Received: 22 October 2013
Revised: 28 January 2014
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.
Mathematics Subject Classification: 65M12 / 65M75 / 65Y05 / 65Y20
Key words: Advection equations / particle methods / semi-Lagrangian methods / GPU computing
© EDP Sciences, SMAI, 2014
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