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Improved ad hoc interface conditions for Schwarz solution procedure tuned to highly heterogeneous media

机译:改进的Schwarz解决方案过程的临时接口条件已调整到高度异构的媒体

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摘要

In this paper, an improved method to derive efficient interface conditions for the Schwarz solution procedure tuned to highly heterogeneous media is presented. This method, based on two parameters optimization, involves new interface conditions specially designed to keep the heterogeneity between the subdomains on the interface. The mathematical analysis of these interface conditions is first presented. Then the asymptotic analysis upon the mesh size parameter together with the heterogeneity ratio is detailed. These interface conditions lead to better asymptotic convergence rate than other available interface conditions. Numerical experiments illustrate the dependence of the proposed method upon several parameters, and confirm the robustness and efficiency of the Schwarz algorithm when equipped with such interface conditions.
机译:在本文中,提出了一种改进的方法,该方法可为已调整为高度异构介质的Schwarz解决方案过程导出有效的接口条件。这种基于两个参数优化的方法涉及专门设计的新接口条件,以保持接口子域之间的异质性。首先介绍了这些界面条件的数学分析。然后详细介绍了网格尺寸参数的渐近分析以及非均质比。与其他可用接口条件相比,这些接口条件导致更好的渐近收敛速度。数值实验说明了该方法对几个参数的依赖性,并在配备了这种接口条件后证实了Schwarz算法的鲁棒性和效率。

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