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

G.-H. Cottet, J.-M. Etancelin, F. Perignon, C. Picard
2014 Mathematical Modelling and Numerical Analysis  
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
more » ... 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.
doi:10.1051/m2an/2014009 fatcat:nxytpvddlbedhahy4znhnkspoa