Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 610398, 12 pages
Research Article

A Computational Realization of a Semi-Lagrangian Method for Solving the Advection Equation

1Institute of Computational Modeling SB RAS, Krasnoyarsk, Akademgorodok 660036, Russia
2Siberian Federal University, Svobodny Prospect, Krasnoyarsk 660041, Russia
3Beihang University, Haidian District, Beijing 100191, China

Received 3 April 2014; Revised 16 August 2014; Accepted 19 August 2014; Published 27 October 2014

Academic Editor: Xiaohui Yuan

Copyright © 2014 Alexander Efremov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture computation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation between time step and mesh size. The theoretical results are confirmed by numerical experiments. Performance of a sequential algorithm and several parallel implementations with the OpenMP and CUDA technologies in the C language has been studied.