Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916381790830592 |
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| author | Bevilacqua, Tommaso Klawonn, Axel Lanser, Martin |
| author_facet | Bevilacqua, Tommaso Klawonn, Axel Lanser, Martin |
| contents | The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and robust preconditioning techniques are necessary for an iterative solution. Here, a balancing domain decomposition by constraints (BDDC) preconditioner is considered. Techniques to enrich the coarse space of BDDC applied to a Stokes problem with heterogeneous viscosity are proposed. In this framework a comparison between two adaptive techniques and a computationally cheaper heuristic approach is carried out. Numerical results computed on a physically realistic model show that the latter approach in combination with the deluxe scaling is a promising alternative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity Bevilacqua, Tommaso Klawonn, Axel Lanser, Martin Numerical Analysis 65F08, 65N30, 65N55 The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and robust preconditioning techniques are necessary for an iterative solution. Here, a balancing domain decomposition by constraints (BDDC) preconditioner is considered. Techniques to enrich the coarse space of BDDC applied to a Stokes problem with heterogeneous viscosity are proposed. In this framework a comparison between two adaptive techniques and a computationally cheaper heuristic approach is carried out. Numerical results computed on a physically realistic model show that the latter approach in combination with the deluxe scaling is a promising alternative. |
| title | Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity |
| topic | Numerical Analysis 65F08, 65N30, 65N55 |
| url | https://arxiv.org/abs/2409.02860 |