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.

翻译：帕拉里尔是一种广泛研究的平行时间方法,可以在某些问题上实现有意义的加速。 但是,众所周知,该方法通常在非阻断式方程式上表现不佳。 本文分析了IMEX Runge- Kutta Parareal 方法在非阻断式方程式上的线性稳定性和趋同性。 通过将标准线性稳定性分析与简单的趋同性分析相结合,我们发现某些半里尔配置可以在非阻断式方程式上实现平行加速。 这些稳定的配置都拥有低迭代数、大块尺寸和大量处理器。 使用非线性施罗德宁格方程式的数值实例显示了分析结论。