Random domain decomposition for parabolic PDEs on graphs
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911130074480640 |
|---|---|
| author | Hernández, Martín |
| author_facet | Hernández, Martín |
| contents | The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch Method (RBM) has shown promise in addressing these challenges via stochastic decomposition techniques. In this paper, we apply the RBM at the PDE level for parabolic equations on graphs, without assuming any preliminary discretization in space or time. We consider a non-overlapping domain decomposition in which the PDE coefficients and source terms are randomized. We prove that the resulting RBM-based scheme converges, in the mean-square sense and uniformly in time, to the true PDE solution with first-order accuracy in the RBM step size. Numerical experiments confirm this convergence rate and demonstrate substantial reductions in both memory usage and computational time compared to solving on the full graph. Moreover, these advantages persist across different time discretization schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random domain decomposition for parabolic PDEs on graphs Hernández, Martín Numerical Analysis Analysis of PDEs 35R02, 65C99, 65M55, 65M75, 68Q25 The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch Method (RBM) has shown promise in addressing these challenges via stochastic decomposition techniques. In this paper, we apply the RBM at the PDE level for parabolic equations on graphs, without assuming any preliminary discretization in space or time. We consider a non-overlapping domain decomposition in which the PDE coefficients and source terms are randomized. We prove that the resulting RBM-based scheme converges, in the mean-square sense and uniformly in time, to the true PDE solution with first-order accuracy in the RBM step size. Numerical experiments confirm this convergence rate and demonstrate substantial reductions in both memory usage and computational time compared to solving on the full graph. Moreover, these advantages persist across different time discretization schemes. |
| title | Random domain decomposition for parabolic PDEs on graphs |
| topic | Numerical Analysis Analysis of PDEs 35R02, 65C99, 65M55, 65M75, 68Q25 |
| url | https://arxiv.org/abs/2508.21557 |