标题： Nyström型指数积分器用于强磁场中的带电粒子动力学 显示英文标题

标题： Nyström Type Exponential Integrators for Strongly Magnetized Charged Particle Dynamics

摘要： 计算带电粒子在电磁场中的动力学（即粒子推进问题）是等离子体物理模拟中粒子-网格（PIC）方法中最计算密集的组成部分之一。当等离子体强烈磁化时，这一任务尤其具有挑战性，因为在这种情况下，粒子运动包含从高度振荡的快速回旋运动到缓慢宏观行为的广泛时间尺度， resulting 的数值模型非常刚性。目前用于模拟粒子运动的最先进的时间积分器由于问题的严重数值刚性而存在局限性，因此需要更高效的 方法。最近，指数积分器被提出作为一种有前景的新方法用于这些模拟，并显示出相对于常用方案的计算优势。指数方法可以精确求解线性问题，并且是$A$稳定的。在本文中，标准指数算法框架被扩展，以推导出一种将牛顿运动方程作为二阶微分方程集成的 Nyström 型指数方法。推导出了二阶和三阶的特定 Nyström 型方案，并应用于强磁化粒子推进问题。数值实验表明，Nyström 型指数积分器在计算效率方面相比标准指数方法有显著提升。 显示英文摘要

摘要： Calculating the dynamics of charged particles in electromagnetic fields (i.e. the particle pushing problem) is one of the most computationally intensive components of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized, since in this case the particle motion consists of a wide range of temporal scales from highly oscillatory fast gyromotion to slow macroscopic behavior and the resulting numerical model is very stiff. Current state-of-the-art time integrators used to simulate particle motion have limitations given the severe numerical stiffness of the problem and more efficient methods are of interest. Recently, exponential integrators have been proposed as a promising new approach for these simulations and shown to offer computational advantages over commonly used schemes. Exponential methods can solve linear problems exactly and are $A$-stable. In this paper, the standard exponential algorithms framework is extended to derive Nystr\"om-type exponential methods that integrate the Newtonian equations of motion as a second-order differential equation. Specific Nystr\"om-type schemes of second and third orders are derived and applied to strongly magnetized particle pushing problems. Numerical experiments are presented to demonstrate that the Nystr\"om-type exponential integrators can provide significant improvement in computational efficiency over the standard exponential methods.