论文标题
IMEX runge-kutta parareal，用于非放射线方程
IMEX Runge-Kutta Parareal for Non-Diffusive Equations
论文作者
论文摘要
Parareal是一种经过广泛研究的并行时间方法，可以在某些问题上实现有意义的加速。但是，众所周知，该方法通常在非扩展方程式上表现较差。本文分析了非扩展方程式上IMEX runge-kutta瘫痪方法的线性稳定性和收敛性。通过将标准线性稳定性分析与简单的收敛分析相结合，我们发现某些瘫痪配置可以在非放射线方程式上实现并行加速。这些稳定的配置都具有较低的迭代计数，大块尺寸和大量处理器。使用非线性Schrodinger方程的数值示例证明了分析结论。
Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.
