基于目标迭代次数的Robin参数优化Schwarz波形松弛的离散时间分析

IF 1.9 3区 数学 Q2 Mathematics
Arthur Arnoult, C. Japhet, P. Omnes
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引用次数: 0

摘要

我们提出了一种新的方法,为抛物问题的优化Schwarz波形松弛(OSWR)迭代的收敛分析提供了新的结果,并允许定义有效的优化Robin参数,该参数依赖于目标迭代计数,这是实际观察到的最优参数共享的属性,而传统的傅里叶分析在时间方向上导致迭代无关的参数。该方法基于时间半离散误差方程的精确解析。它允许推荐一对(迭代次数,Robin参数)来达到给定的精度。虽然一般的思想可以适用于任意的空间维度,但本文首先在一维情况下进行分析。数值实验验证了这种迭代相关优化Robin参数所获得的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Discrete-time analysis of optimized Schwarz waveform relaxation with Robin parameters depending on the targeted iteration count
We propose a new approach that provides new results in the convergence analysis of optimized Schwarz waveform relaxation (OSWR) iterations for parabolic problems, and allows to define efficient optimized Robin parameters that depend on the targeted iteration count, a property that is shared by the actual observed optimal parameters, while traditional Fourier analysis in the time direction leads to iteration independent parameters. This new approach is based on the exact resolution of the time semi-discrete error equations. It allows to recommend a couple (number of iterations, Robin parameter) to reach a given accuracy. While the general ideas may apply to an arbitrary space dimension, the analysis is first presented in the one dimensional case. Numerical experiments illustrate the performance obtained with such iteration-dependent optimized Robin parameters.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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