关于 Parareal 与 MGRIT 应用于线性平流方程时粗网格算子的选取
数值分析
2019-10-15 v2 数值分析
摘要
我们考虑用 Parareal 和两层 multigrid-reduction-in-time（MGRIT）算法对线性平流方程进行并行时间积分。我们的目标是更好地理解这些算法对该问题的收敛行为，已知其相对于扩散方程（其模型抛物型对应问题）表现较差。利用傅里叶分析，我们推导了这些算法的新的收敛估计，结合现有收敛理论，可深入洞察此不佳性能的起源。我们随后使用该理论探索改进的粗网格时间步进算子。对于平流方程的若干高阶离散化，我们证明了存在非标准粗网格时间步进算子，相较标准重离散化选择可带来显著改进。
引用
@article{arxiv.1902.07757,
title = {On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection},
author = {Oliver A. Krzysik and Hans De Sterck and Scott P. MacLachlan and Stephanie Friedhoff},
journal= {arXiv preprint arXiv:1902.07757},
year = {2019}
}
备注
This work was submitted to the Student Paper Competition of the 19th Copper Mountain Conference On Multigrid Methods, Copper Mountain, CO, USA. Much of this manuscript has formed the foundations of a full-length manuscript for which a preprint is available at arXiv:1910.03726