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Towards optimal explicit time-stepping schemes for the gyrokinetic equations

机译：寻求动力学方程的最佳显式时间步长方案

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摘要

The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes measures to improve the efficiency of such computations, thereby making them more realistic. Explicit Runge-Kutta schemes are considered to be well suited for time-stepping. Although the numerical algorithms are often highly optimized, performance can still be improved by a suitable choice of the time-stepping scheme, based on the spectral analysis of the underlying operator. Here, an operator splitting technique is introduced to combine first-order Runge-Kutta-Chebychev schemes for the collision term with fourth-order schemes for the remaining terms. In the nonlinear regime, based on the observation of eigenvalue shifts due to the (generalized) E×B advection term, an accurate and robust estimate for the nonlinear timestep is developed. The presented techniques can reduce simulation times by factors of up to three in realistic cases. This substantial speedup encourages the use of similar timestep optimized explicit schemes not only for the gyrokinetic equation, but also for other applications with comparable properties.
机译：非线性动力学方程描述了实验室和天体等离子体中的等离子体湍流。为了解决这些方程，已经开发了大规模并行代码并在当今的超级计算机上运行。本文介绍了可提高此类计算效率的措施，从而使其更加现实。明确的Runge-Kutta方案被认为非常适合时间步长。尽管数值算法通常经过高度优化，但仍可以根据基础算符的频谱分析，通过适当选择时间步进方案来提高性能。在这里，引入了算子拆分技术，以将碰撞项的一阶Runge-Kutta-Chebychev方案与其余项的四阶方案相结合。在非线性状态下，基于对（广义）E×B对流项的特征值偏移的观察，开发了非线性时间步长的准确且鲁棒的估计。在实际情况下，所提出的技术可以将模拟时间减少多达三倍。这种实质性的加速不仅鼓励将相似的时步优化显式方案用于陀螺动力学方程，而且还用于具有可比特性的其他应用。

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