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Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay
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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BibTeX
@misc{tomer2026neumannneumann,
title = {{Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay}},
author = {Deeksha Tomer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11098},
eprint = {2609.11098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11098},
}
RIS
TY - UNPB
TI - Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay
AU - Deeksha Tomer
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11098
UR - https://arxiv.org/abs/2609.11098
AB - 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.
ER -