Computational methods are needed in plasma physics to understand and simulate magnetically confined plasmas
The fundamental equations used to understand and predict various phenomena in plasma physics share a very important feature: They are all nonlinear. This implies that analytical techniques - although also very important - are limited in practice, calling for a numerical approach.
Fortunately, the capabilities of modern supercomputers have reached a level which allows to tackle some outstanding open issues in theoretical plasma physics, including, e.g., turbulence, nonlinear magnetohydrodynamics, and plasma-wall interaction.
Given the multiscale nature of most problems of interest, advanced algorithms and efficient implementations on massively parallel platforms are usually required in order to tackle them. In this context, a close collaboration of theoretical plasma physicists with applied mathematicians and computer scientists can be of great benefit. Thus, state-of-the-art numerical techniques, hardware-aware implementation strategies, and scalable parallelization approaches are explored in terms of their potential to minimize the overall computational requirements and to maximize the reliability and robustness of the simulations.
A recent successful example is a project dealing with the fast solution of linear eigenvalue problems in the framework of gyrokinetic theory.
The usage of a Jacobi-Davidson eigenvalue solver in combination with a preconditioner based on an approximate explicit representation of the linear gyrokinetic operator allowed for a speed-up of more than two orders of magnitude compared with the initially employed method. Thus, detailed investigations of eigenmodes in multidimensional parameter spaces are now feasible, contributing to a better understanding of the drive and dissipation mechanisms of turbulent fusion plasmas.