Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for PDEs with Time Delay
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929468840345600 |
|---|---|
| author | Tomer, Deeksha Mandal, Bankim Chandra |
| author_facet | Tomer, Deeksha Mandal, Bankim Chandra |
| contents | We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively), tailored for solving partial differential equations (PDEs) incorporating time delay. Time delay phenomena frequently arise in various real-world systems, making their accurate modeling and simulation crucial for understanding and prediction. We consider a series of model problems, ranging from Parabolic, Hyperbolic to Neutral PDEs with time delay and apply the iterative techniques DNWR and NNWR for solving in parallel. We present the theoretical foundations, numerical implementation, and comparative performance analysis of these two methods. Through numerical experiments and simulations, we explore their convergence properties, computational efficiency, and applicability to various types of PDEs with time delay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11171 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for PDEs with Time Delay Tomer, Deeksha Mandal, Bankim Chandra Numerical Analysis Analysis of PDEs We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively), tailored for solving partial differential equations (PDEs) incorporating time delay. Time delay phenomena frequently arise in various real-world systems, making their accurate modeling and simulation crucial for understanding and prediction. We consider a series of model problems, ranging from Parabolic, Hyperbolic to Neutral PDEs with time delay and apply the iterative techniques DNWR and NNWR for solving in parallel. We present the theoretical foundations, numerical implementation, and comparative performance analysis of these two methods. Through numerical experiments and simulations, we explore their convergence properties, computational efficiency, and applicability to various types of PDEs with time delay. |
| title | Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for PDEs with Time Delay |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2408.11171 |