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CADD: A seamless solution to the Domain Decomposition problem of subdomain boundaries and cross-points
Wave Motion ( IF 2.4 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.wavemoti.2020.102649
Dan Gordon , Rachel Gordon

Abstract The solution of wave problems using Domain Decomposition (DD) requires that the subdomain boundaries should be virtually non-existent, so that waves are not affected by the boundaries. This is a primary problem in DD, and it intensifies in the case of cross-points at which three or more subdomains meet. This topic has received a lot of attention in recent years, with special treatment of cross-points. This paper explains and demonstrates that this problem does not exist in Component-Averaged Domain Decomposition (CADD). CADD is implemented here with the authors’ CARP-CG algorithm, but it is shown that other implementations are also possible. The reason for the non-existence of this problem in CARP-CG is that in some superspace of the problem space, CARP-CG is mathematically equivalent to the CG acceleration of the Kaczmarz algorithm with cyclic relaxation parameters, applied to a single linear system. Due to its advantages, CARP-CG was adopted by some geophysics researchers as the solver of the Helmholtz and the elastic wave equations for full waveform inversion (FWI).

中文翻译:

CADD:子域边界和交叉点的域分解问题的无缝解决方案

摘要 使用域分解(DD)解决波浪问题要求子域边界几乎不存在,从而使波浪不受边界的影响。这是 DD 中的主要问题,并且在三个或更多子域相遇的交叉点的情况下会加剧。这个话题近年来受到了很多关注,对交叉点进行了特殊处理。这篇论文解释并证明了这个问题在分量平均域分解(CADD)中不存在。此处使用作者的 CARP-CG 算法实现了 CADD,但表明其他实现也是可能的。CARP-CG中不存在这个问题的原因是在问题空间的某个超空间中,CARP-CG 在数学上等同于 Kaczmarz 算法的 CG 加速度,带有循环松弛参数,应用于单个线性系统。由于CARP-CG的优势,一些地球物理研究人员采用CARP-CG作为亥姆霍兹方程和全波形反演(FWI)弹性波方程的求解器。
更新日期:2020-11-01
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