Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916382796414976 |
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| author | Klawonn, Axel Lanser, Martin |
| author_facet | Klawonn, Axel Lanser, Martin |
| contents | Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex problems. In this article, a nonlinear two-level Schwarz approach is considered and, for the first time, equipped with monolithic GDSW (Generalized Dryja-Smith-Widlund) coarse basis functions for the Navier-Stokes equations. Results for lid-driven cavity problems with high Reynolds numbers are presented and compared with classical global Newton's method equipped with a linear Schwarz preconditioner. Different options, for example, local pressure corrections on the subdomain and recycling of coarse basis functions are discussed in the nonlinear Schwarz approach for the first time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations Klawonn, Axel Lanser, Martin Numerical Analysis Computational Engineering, Finance, and Science 65F08, 65F10, 65H10, 65N22, 65N55, 76-10 Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex problems. In this article, a nonlinear two-level Schwarz approach is considered and, for the first time, equipped with monolithic GDSW (Generalized Dryja-Smith-Widlund) coarse basis functions for the Navier-Stokes equations. Results for lid-driven cavity problems with high Reynolds numbers are presented and compared with classical global Newton's method equipped with a linear Schwarz preconditioner. Different options, for example, local pressure corrections on the subdomain and recycling of coarse basis functions are discussed in the nonlinear Schwarz approach for the first time. |
| title | Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations |
| topic | Numerical Analysis Computational Engineering, Finance, and Science 65F08, 65F10, 65H10, 65N22, 65N55, 76-10 |
| url | https://arxiv.org/abs/2409.03041 |