On the stability of exponential integrators for non-diffusive equations
On the stability of exponential integrators for non-diffusive equations
复制标题
非扩散方程指数积分器的稳定性
DOI：
10.1016/j.cam.2022.114126
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Minion, Michael L.
中科院分区：
文献类型：
--
作者：
Buvoli, Tommaso;Minion, Michael L.
指数积分器是一类众所周知的时间积分方法，在过去的二十年中已经成为许多研究和发展的主题。令人惊讶的是，迄今为止，分析它们在非扩散方程上的稳定性和效率的努力有限。本文应用线性稳定性分析来证明指数积分器在非扩散问题上的不稳定性。然后，我们提出了一种简单的重划分方法，该方法稳定了积分器，并使刚性非扩散方程的有效解成为可能。为了验证我们方法的有效性，我们进行了几个数值实验，将分区指数积分器与未修改指数积分器进行比较。我们还将重新划分与众所周知的在等式右侧添加高粘度的方法进行了比较。总的来说，我们发现重新划分恢复了大时间步长的收敛性，并且与高粘度不同，它不需要使用高阶空间导数。
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and efficiency on non-diffusive equations to date. In this paper we apply linear stability analysis to showcase the poor stability properties of exponential integrators on non-diffusive problems. We then propose a simple repartitioning approach that stabilizes the integrators and enables the efficient solution of stiff, non-diffusive equations. To validate the effectiveness of our approach, we perform several numerical experiments that compare partitioned exponential integrators to unmodified ones. We also compare repartitioning to the well-known approach of adding hyperviscosity to the equation right-hand-side. Overall, we find that the repartitioning restores convergence at large timesteps and, unlike hyperviscosity, it does not require the use of high-order spatial derivatives.