Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916463481192448 |
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| author | Heinlein, Alexander Ho, Kyrill Klawonn, Axel Lanser, Martin |
| author_facet | Heinlein, Alexander Ho, Kyrill Klawonn, Axel Lanser, Martin |
| contents | Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method converges slowly or not at all. This article introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on the FROSch (Fast and Robust Overlapping Schwarz) solver framework, part of Sandia's Trilinos library. First, an introduction to the key concepts underlying two-level nonlinear Schwarz methods is given, including a brief overview of the coarse space used to build the second level. Next, the parallel implementation is discussed, followed by preliminary parallel results for a scalar nonlinear diffusion problem and a 2D nonlinear plane-stress Neo-Hooke elasticity problem with large deformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch Heinlein, Alexander Ho, Kyrill Klawonn, Axel Lanser, Martin Numerical Analysis 65F08, 65F10, 65H10, 65N22, 65N55 Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method converges slowly or not at all. This article introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on the FROSch (Fast and Robust Overlapping Schwarz) solver framework, part of Sandia's Trilinos library. First, an introduction to the key concepts underlying two-level nonlinear Schwarz methods is given, including a brief overview of the coarse space used to build the second level. Next, the parallel implementation is discussed, followed by preliminary parallel results for a scalar nonlinear diffusion problem and a 2D nonlinear plane-stress Neo-Hooke elasticity problem with large deformations. |
| title | Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch |
| topic | Numerical Analysis 65F08, 65F10, 65H10, 65N22, 65N55 |
| url | https://arxiv.org/abs/2410.24138 |