A Parallel-in-Time Combination Method for Parabolic Problems
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917449234907136 |
|---|---|
| author | Griebel, Michael Schweitzer, Marc Alexander Troska, Lukas |
| author_facet | Griebel, Michael Schweitzer, Marc Alexander Troska, Lukas |
| contents | In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with its implementation in the library XBraid, the sparse grid combination method for discretizing the resulting elliptic problems in space, and a domain decomposition method for each of the subproblems in the combination method based on the space-filling curve approach. As a result, we obtain an extremely fast and embarrassingly parallel solver with excellent speedup and scale-up qualities, which is perfectly suited for parabolic problems with up to six space dimensions. We describe our new parallel approach and show its superior parallelization properties for the heat equation, the chemical master equation and some exemplary stochastic differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Parallel-in-Time Combination Method for Parabolic Problems Griebel, Michael Schweitzer, Marc Alexander Troska, Lukas Numerical Analysis 65M55, 65M22, 65M99, 65F08, 65Y05, 65Y99 In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with its implementation in the library XBraid, the sparse grid combination method for discretizing the resulting elliptic problems in space, and a domain decomposition method for each of the subproblems in the combination method based on the space-filling curve approach. As a result, we obtain an extremely fast and embarrassingly parallel solver with excellent speedup and scale-up qualities, which is perfectly suited for parabolic problems with up to six space dimensions. We describe our new parallel approach and show its superior parallelization properties for the heat equation, the chemical master equation and some exemplary stochastic differential equations. |
| title | A Parallel-in-Time Combination Method for Parabolic Problems |
| topic | Numerical Analysis 65M55, 65M22, 65M99, 65F08, 65Y05, 65Y99 |
| url | https://arxiv.org/abs/2509.22156 |