Wavelet-based edge multiscale parareal algorithm for parabolic equations with heterogeneous coefficients and rough initial data

JOURNAL OF COMPUTATIONAL PHYSICS

卷:444

Article

Li, Guanglian¹  Hu, Jiuhua² 

[1] Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Peoples R China

[2] Texas A&M Univ, Dept Math, College Stn 77843, TX USA

关键词: Multiscale;    Heterogeneous;    Wavelets;    Parareal;    Rough initial data;    Parabolic;   

DOI  :  10.1016/j.jcp.2021.110572

来源: Elsevier

【 摘 要 】

We propose in this paper the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm to solve parabolic equations with heterogeneous coefficients efficiently. This algorithm combines the advantages of multiscale methods that can deal with heterogeneity in the spatial domain effectively, and the strength of parareal algorithms for speeding up time evolution problems when sufficient processors are available. We derive the convergence rate of this algorithm in terms of the mesh size in the spatial domain, the level parameter used in the multiscale method, the coarse-scale time step and the fine-scale time step. Extensive numerical tests are presented to demonstrate the performance of our algorithm, which verify our theoretical results perfectly. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free