Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay

Deeksha Tomer

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arXiv · 2609.11098

Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay

Deeksha Tomer

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Abstract

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.

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Deeksha Tomer. 2026-09-10. Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay. https://arxiv.org/abs/2609.11098

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