Geometric adaptive smoothed aggregation multigrid for discontinuous Galerkin discretisations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912403200933888 |
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| author | Pan, Yulong Lindsey, Michael Persson, Per-Olof |
| author_facet | Pan, Yulong Lindsey, Michael Persson, Per-Olof |
| contents | We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully unstructured meshes using arbitrary element shapes. Furthermore, the method can be employed for a wide range of commonly used DG numerical fluxes for first- and second-order PDEs including the Interior Penalty and the Local Discontinuous Galerkin methods. We demonstrate excellent and mesh-independent convergence for a range of problems including the Poisson equation, and convection-diffusion for a range of Péclet numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric adaptive smoothed aggregation multigrid for discontinuous Galerkin discretisations Pan, Yulong Lindsey, Michael Persson, Per-Olof Numerical Analysis 65N30, 65N55 We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully unstructured meshes using arbitrary element shapes. Furthermore, the method can be employed for a wide range of commonly used DG numerical fluxes for first- and second-order PDEs including the Interior Penalty and the Local Discontinuous Galerkin methods. We demonstrate excellent and mesh-independent convergence for a range of problems including the Poisson equation, and convection-diffusion for a range of Péclet numbers. |
| title | Geometric adaptive smoothed aggregation multigrid for discontinuous Galerkin discretisations |
| topic | Numerical Analysis 65N30, 65N55 |
| url | https://arxiv.org/abs/2504.13373 |