PhD thesis : Parallel computation and numerical schemes for boundary plasma simulation

PhD defense : Matthieu KUHN

Team : ICPS

Title : Parallel computation and numerical schemes for boundary plasma simulation

Abstract :  Controlled thermonuclear fusion has several advantages, nevertheless simulations are required in order to reach an industrial scale. In particular, a better knowledge of turbulent transport taking place at the edges of tokamaks is important to ensure the confinement quality, and hence the reactor performances. On this issue, plasma boundary simulations represent a major stake. To adress characteristic physical phenomena appearing at large time scales (as those of the ELMs or the transport barriers) and at a relatively small spatial case (magnetic islands), high computational cost are induced. Typical simulations can require several months on a single processing unit. Tools with such settings are not really easily usable. The code that has been the main target is Emedge3D. This PhD thesis proposes improvements of some numerical schemes to shorten time to solution for the physicists that use this code, and also describes parallel algorithms to use multiple processing units.
On the numerical scheme side, Emedge3D is close to the classical advection-diffusion problem. Using standard solutions and explicit integration time methods, a hard stability condition is imposed on the time step. Furthermore, in the kind of models that we consider, the diffusion operator is anisotropic: it is stronger in the parallel direction to the magnetic field lines (compared to to the perpendicular direction). One result of this work is a solution to better control the error produced by the anisotropic diffusion solver. Regarding the computational cost side, we look at the memory bandwidth limitation, partly caused by the switching between two 3D spatial discretizations: real and Fourier variables. Finally, non linear operators (Poisson brackets) are computed with a well known method (Arakawa), whose stencil implies a high computational cost.
The improvements of Emedge3D are along two axes. On the first hand, we bring innovations concerning the numerical methods used. Concerning the time integration scheme, we show what are the benefits of semi-implicit methods. Their unconditional stable property allows one to consider larger time step values, diminishing the time needed to perform simulations. In particular, a new class of semi-implicit method is described and compared to several other semi-implicit methods on different test cases. Then, we show the importance of using high order methods in time and in space. This allows one to control the additional error produced by the larger time step.
On the second hand, we propose solutions for the parallelization of the Emedge3D code. A first parallelization has been done targeting shared memory architectures. A memory bandwidth limitation is observed, techniques are shown to overcome it. However, for one part of the code, the performance is not satisfactory enough and also, the number of processing units available in one shared memory node remains usually low. Hence, a parallelization study on distributed memory architecture is presented. Adding computational nodes allows one to increase the total memory bandwidth and computing units. This last study is performed on the more general non linear advection-diffusion problem, very close to the mathematical structure of the Emedge3D equations.
This PhD thesis is part of an interdisciplinary ANR project, named E2T2, that operates on the Emedge3D code and other related topics. This code is developed for several years in the PIIM physics laboratory (Aix-Marseille University).

The presentation will take place on Monday September 29th at 2.00pm in room A207 of the Pôle API building in Illkirch.