A new characterization of the convergence factor of two-level methods
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866908389815091200 |
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| author | Xu, Xuefeng |
| author_facet | Xu, Xuefeng |
| contents | Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis and design of multilevel methods. In this paper, we present a concise and easy-to-use identity for characterizing the convergence factor of two-level methods, whose hierarchical spaces can be either overlapping or non-overlapping. In order to illustrate its usability and convenience, we give several applications, which offer new insights into the design of multilevel methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_08600 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A new characterization of the convergence factor of two-level methods Xu, Xuefeng Numerical Analysis Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis and design of multilevel methods. In this paper, we present a concise and easy-to-use identity for characterizing the convergence factor of two-level methods, whose hierarchical spaces can be either overlapping or non-overlapping. In order to illustrate its usability and convenience, we give several applications, which offer new insights into the design of multilevel methods. |
| title | A new characterization of the convergence factor of two-level methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2102.08600 |