SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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A novel, semilagrangian, coarse solver for the parareal technique and its application to 2D drift-wave (BETA) and 5D gyrokinetic (GENE), turbulence simulations

J.M. Reynolds-Barredo, D.E. Newman, R. Sanchez and F. Jenko

Abstract
In this work, we apply parareal [1] to convection dominated problems. In particular, to a 2D drift waves case using BETA code and in a 5D gyrokinetic simulation using GENE code. Partial success was previously reported [2] but, here, a new and promissing coarse solver based on semilagrangian time advance is proposed and tested on both kind of simulations. The advantage of the semilagrangian solver is that it can be split into a piece that can run in parallel (the computation of the interpolation coefficients) and a piece that is computed serially (the application of the coefficients over the convected field). The second piece is the time limiting part (due to its sequential character) but can be computed much faster than the fine solver.

Bibliography
[1] J. Lions, Y. Maday and G. Turinici, CR Acad. Sci. I - Math 332 (7) 661 (2001)
[2] D. Samaddar, D.E. Newman and R. Sanchez, J. Comput. Phys. 229, 6558 (2010)

Organized by         Universidad de Valladolid     IMUVA