IMEX Runge-Kutta Parareal for Non-diffusive Equations
IMEX Runge-Kutta Parareal for Non-diffusive Equations
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DOI：
10.1007/978-3-030-75933-9_5
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
Tommaso Buvoli;M. Minion
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文献类型：
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作者：
Tommaso Buvoli;M. Minion
Parareal是一种被广泛研究的时间并行方法，可以在某些问题上实现有意义的加速。然而，众所周知，该方法通常在非扩散方程上表现不佳。本文分析了非扩散方程IMEX Runge-Kutta Parareal方法的线性稳定性和收敛性。通过结合标准的线性稳定性分析和简单的收敛性分析，我们发现某些Parareal配置可以实现非扩散方程的并行加速。这些稳定的配置具有低迭代次数，大的块大小和大量的处理器。利用非线性薛定谔方程的数值例子验证了分析结论。
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 possess low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrödinger equation demonstrate the analytical conclusions.