A hybrid algorithm based on parareal and Schwarz waveform relaxation-Reference-Cited by-同舟云学术

A hybrid algorithm based on parareal and Schwarz waveform relaxation

Published:2022 Issue:11 Volume:30 Page:4086-4107
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Yang Liping¹,Li Hu²

Affiliation:

1. Department of Mathematics, Zigong Vocational and Technical College, Zigong 643000, China

2. School of Mathematics, Chengdu Normal University, Chengdu 611130, China

Abstract

<abstract><p>In this paper, we present a hybrid algorithm based on parareal and Schwarz waveform relaxation (SWR) for solving time dependent partial differential equations. The parallelism can be simultaneously realized in the time direction by using a parareal and in the space direction via SWR. We give a convergence analysis for the hybrid algorithm for a 1D model problem, the reaction-diffusion equation. Weak scaling of the algorithm in terms of both the number of space subdomains and the number of paralleled time intervals were investigated via theoretical analysis and numerical experiments.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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