Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915370852417536 |
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| author | Nataf, Frédéric Parolin, Emile |
| author_facet | Nataf, Frédéric Parolin, Emile |
| contents | Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of adaptive coarse spaces we present here is quite general since it applies to symmetric and non-symmetric problems, to symmetric preconditioners such as the additive Schwarz method (ASM) and to the non-symmetric preconditioner restricted additive Schwarz (RAS), as well as to exact or inexact subdomain solves. The coarse space is built by solving generalized eigenproblems in the subdomains and applying a well-chosen operator to the selected eigenvectors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_02758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems Nataf, Frédéric Parolin, Emile Numerical Analysis 65F08, 65F10, 65N22, 65N30, 65N55, 65Y05 Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of adaptive coarse spaces we present here is quite general since it applies to symmetric and non-symmetric problems, to symmetric preconditioners such as the additive Schwarz method (ASM) and to the non-symmetric preconditioner restricted additive Schwarz (RAS), as well as to exact or inexact subdomain solves. The coarse space is built by solving generalized eigenproblems in the subdomains and applying a well-chosen operator to the selected eigenvectors. |
| title | Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems |
| topic | Numerical Analysis 65F08, 65F10, 65N22, 65N30, 65N55, 65Y05 |
| url | https://arxiv.org/abs/2404.02758 |