带时滞双曲偏微分方程的Neumann-Neumann波形松弛方法

中文摘要 AI 辅助

带时滞的双曲偏微分方程对于建模广泛的现实世界应用至关重要。由于通常无法获得闭式解，开发准确且高效的数值方法变得至关重要。本文针对非均匀子域划分情形，实现了一种新颖的子结构波形松弛方法，即Neumann-Neumann波形松弛（NNWR）方法，用于数值求解双曲时滞偏微分方程。首先利用傅里叶分析对其收敛行为进行分析以获得估计，随后通过拉普拉斯变换技术证明了有限步收敛性。文中给出了各种测试案例作为数值示例。

英文摘要

Hyperbolic PDEs with time delay are essential for modeling a wide range of real-world applications. Since closed-form solutions are often not attainable, developing accurate and efficient numerical methods becomes crucial. In this work a novel substructuring waveform relaxation method namely Neumann-Neumann Waveform Relaxation (NNWR) has been implemented for numerically solving hyperbolic delay PDEs in the case of non-uniform subdomain partitioning. The convergence behavior is first analyzed using Fourier analysis to obtain an estimate, followed by a demonstration of finite-step convergence through Laplace transform techniques. Various test cases are presented as numerical illustrations.

发表机构

• Indian Institute of Technology Bhubaneswar（印度理工学院布巴内斯瓦尔分校）

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