抛物线最优控制问题的新时域分解方法 II：诺伊曼-诺伊曼算法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Numerical Analysis Pub Date : 2024-11-19 DOI:10.1137/24m1634424

Martin J. Gander, Liu-Di Lu

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引用次数: 0

摘要

SIAM 数值分析期刊》，第 62 卷，第 6 期，第 2588-2610 页，2024 年 12 月。摘要。我们建议使用 Neumann-Neumann 算法对无约束线性抛物线最优控制问题进行时间并行求解。我们研究了九种变体，分析了它们的收敛行为，并确定了每种变体的最佳松弛参数。我们的研究结果表明，虽然最直观的诺伊曼-诺伊曼算法是有效的平滑器，但还有更高效的诺伊曼-诺伊曼求解器可用。我们通过数值实验来支持我们的分析。

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New Time Domain Decomposition Methods for Parabolic Optimal Control Problems II: Neumann–Neumann Algorithms

SIAM Journal on Numerical Analysis, Volume 62, Issue 6, Page 2588-2610, December 2024.
Abstract. We propose to use Neumann–Neumann algorithms for the time parallel solution of unconstrained linear parabolic optimal control problems. We study nine variants, analyze their convergence behavior, and determine the optimal relaxation parameter for each. Our findings indicate that while the most intuitive Neumann–Neumann algorithms act as effective smoothers, there are more efficient Neumann–Neumann solvers available. We support our analysis with numerical experiments.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.