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

Author

Listed:
  • Alexander Efremov
  • Eugeniya Karepova
  • Vladimir Shaydurov
  • Alexander Vyatkin

Abstract

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.

Suggested Citation

  • Alexander Efremov & Eugeniya Karepova & Vladimir Shaydurov & Alexander Vyatkin, 2014. "A Computational Realization of a Semi‐Lagrangian Method for Solving the Advection Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:610398
    DOI: 10.1155/2014/610398
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    References listed on IDEAS

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    1. Elisabetta Carlini & Maurizio Falcone & Roberto Ferretti, 2006. "A Time—Adaptive Semi—Lagrangian Approximation to Mean Curvature Motion," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 732-739, Springer.
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