On an efficient line smoother for the p-multigrid γ-cycle
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916770187575296 |
|---|---|
| author | Lorca, José Pablo Lucero Rosenberg, Duane Jankov, Isidora McCoid, Conor Gander, Martin Jakob |
| author_facet | Lorca, José Pablo Lucero Rosenberg, Duane Jankov, Isidora McCoid, Conor Gander, Martin Jakob |
| contents | As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear system arising from a Gauss-Legendre-Lobatto global spectral method. We precondition using a p-multigrid γ-cycle with highly-vectorizable smoothers, that we refer to as line smoothers. Our smoothers are restrictions of spectral and finite element discretizations to low-order one-dimensional problems along lines, that are solved by a reformulation of cyclic reduction as a direct multigrid method. We illustrate our method with numerical experiments showing the apparent boundedness of the iteration count for a fixed residual reduction over a range of moderately deformed domains, right hand sides and Dirichlet boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On an efficient line smoother for the p-multigrid γ-cycle Lorca, José Pablo Lucero Rosenberg, Duane Jankov, Isidora McCoid, Conor Gander, Martin Jakob Numerical Analysis 65N35 As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear system arising from a Gauss-Legendre-Lobatto global spectral method. We precondition using a p-multigrid γ-cycle with highly-vectorizable smoothers, that we refer to as line smoothers. Our smoothers are restrictions of spectral and finite element discretizations to low-order one-dimensional problems along lines, that are solved by a reformulation of cyclic reduction as a direct multigrid method. We illustrate our method with numerical experiments showing the apparent boundedness of the iteration count for a fixed residual reduction over a range of moderately deformed domains, right hand sides and Dirichlet boundary conditions. |
| title | On an efficient line smoother for the p-multigrid γ-cycle |
| topic | Numerical Analysis 65N35 |
| url | https://arxiv.org/abs/2504.10710 |