论文标题
基于插值的多余runge-kutta-chebyshev方法的不稳定性和降低现象
Instabilities and order reduction phenomenon of an interpolation based multirate Runge-Kutta-Chebyshev method
论文作者
论文摘要
提出了明确的稳定添加剂kutta方案。该方法基于严重僵硬且僵硬的子问题的分裂，然后使用runge-kutta-chebyshev方案独立解决。根据子问题的刚度对阶段的数量进行调整，并导致需要幽灵值的异步集成。每当需要幽灵值时，都会使用阶段之间的时间性插值。该方案的一种重要应用是在不均匀网格上离散的抛物线偏微分方程。本文的目的是介绍该方案并在模型问题上证明线性插值触发不稳定性。此外，我们表明它具有减少秩序现象。理论结果在数值上得到确认。
An explicit stabilized additive Runge-Kutta scheme is proposed. The method is based on a splitting of the problem in severely stiff and mildly stiff subproblems, which are then independently solved using a Runge-Kutta-Chebyshev scheme. The number of stages is adapted according to the subproblem's stiffness and leads to asynchronous integration needing ghost values. Whenever ghost values are needed, linear interpolation in time between stages is employed. One important application of the scheme is for parabolic partial differential equations discretized on a nonuniform grid. The goal of this paper is to introduce the scheme and prove on a model problem that linear interpolations trigger instabilities into the method. Furthermore, we show that it suffers from an order reduction phenomenon. The theoretical results are confirmed numerically.
