A Framework for the Solution of Tree-Coupled Saddle-Point Systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916461872676864 |
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| author | Hansknecht, Christoph Heinzelreiter, Bernhard Pearson, John W. Potschka, Andreas |
| author_facet | Hansknecht, Christoph Heinzelreiter, Bernhard Pearson, John W. Potschka, Andreas |
| contents | We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then propose several structure-exploiting preconditioners to be used during applications of the MINRES and GMRES algorithms and analyze their properties. We adapt several concepts originating in the field of multigrid methods, obtaining a variety of problem-adapted multi-level methods. We analyze the complexity of all algorithms, and derive a number of results on eigenvalues of the preconditioned system and convergence of iterative methods. We validate our theoretical findings through a range of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23385 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Framework for the Solution of Tree-Coupled Saddle-Point Systems Hansknecht, Christoph Heinzelreiter, Bernhard Pearson, John W. Potschka, Andreas Numerical Analysis Optimization and Control We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then propose several structure-exploiting preconditioners to be used during applications of the MINRES and GMRES algorithms and analyze their properties. We adapt several concepts originating in the field of multigrid methods, obtaining a variety of problem-adapted multi-level methods. We analyze the complexity of all algorithms, and derive a number of results on eigenvalues of the preconditioned system and convergence of iterative methods. We validate our theoretical findings through a range of numerical experiments. |
| title | A Framework for the Solution of Tree-Coupled Saddle-Point Systems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2410.23385 |