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

Published online by Cambridge University Press:  30 June 2014

G.-H. Cottet ,
J.-M. Etancelin ,
F. Perignon  and
C. Picard
G.-H. Cottet
Affiliation:
UniversitéGrenoble Alpes and CNRS, Laboratoire Jean Kuntzmann, BP 53 38041, Grenoble Cedex 9, France. georges-henri.cottet@imag.fr
J.-M. Etancelin
Affiliation:
UniversitéGrenoble Alpes and CNRS, Laboratoire Jean Kuntzmann, BP 53 38041, Grenoble Cedex 9, France. georges-henri.cottet@imag.fr
F. Perignon
Affiliation:
UniversitéGrenoble Alpes and CNRS, Laboratoire Jean Kuntzmann, BP 53 38041, Grenoble Cedex 9, France. georges-henri.cottet@imag.fr
C. Picard
Affiliation:
UniversitéGrenoble Alpes and CNRS, Laboratoire Jean Kuntzmann, BP 53 38041, Grenoble Cedex 9, France. georges-henri.cottet@imag.fr
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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.

Keywords

Advection equationsparticle methodssemi-Lagrangian methodsGPU computing
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 4 , July 2014 , pp. 1029 - 1060
Copyright
© EDP Sciences, SMAI, 2014

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