A novel, semilagrangian, coarse solver for the Parareal technique and its application to 2D fluid drift-wave (BETA) and 5D gyrokinetic (GENE), turbulence simulations
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In this work, we apply the Parareal time-parallelization technique [1] to convection-dominated problems. In particular, to a 2D drift-waves case using the BETA code and to a 5D gyro-kinetic ITG simulation using GENE code. Although partial success was previously reported applying parareal to the drift-wave BETA runs [2], the speed-up of the process was limited by the compromise that must be reached between having a sufficiently fast coarse serial solver for the problem, and how far from the actual solution the coarse solver is pushed by the approximations made. This limitation becomes more dramatic in the case of GENE simulations. Here, we propose and test a new and promising coarse solver based on a semi-lagrangian time advance. Its advantage comes from the fact that a significant part of the coarse solver can be solved in parallel. As a result, it can be made faster without paying the penalty of excessive simplifications. Introduction to Parareal Generally, physical problems simulated on a computer can be efficiently parallelized only up to a certain number of processors. With the supercomputers that are available nowadays, there are often many more processors available then the number that can be efficiently utilized with standard techniques. It is therefore clear that new parallelization techniques that permit to increase the number of processors are of great interest. Parareal [1] is a new such parallelization technique that focuses on the time coordinate. It is based on an iterative process with two stages for every iteration: 1) a fast coarse time propagator that gives an approximated solution for all time; 2) an accurate time propagator that is used to correct the solution. The first stage is fast but must be computed sequentially. The second one is expensive but can be computed in parallel. The key to success depends on choosing an adequate coarse solver: it must be much faster than the fine one but, at the same time, not diverge too much from the actual solution. We introduce next the algorithm with more detail, but we refer the reader to [3] for a more in-depth description. In general, we will look for the solution represented by the state vector 40 EPS Conference on Plasma Physics P4.162