Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem
We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/5/452 |
| _version_ | 1827742022815973376 |
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| author | Durkbin Cho |
| author_facet | Durkbin Cho |
| author_sort | Durkbin Cho |
| collection | DOAJ |
| description | We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters. |
| first_indexed | 2024-03-11T03:56:22Z |
| format | Article |
| id | doaj.art-0fac4abe866341fabb1f942f1b1d8d4f |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T03:56:22Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-0fac4abe866341fabb1f942f1b1d8d4f2023-11-18T00:27:29ZengMDPI AGAxioms2075-16802023-05-0112545210.3390/axioms12050452Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic ProblemDurkbin Cho0Department of Mathematics, Dongguk University, Pil-dong 3-ga, Jung-gu, Seoul 04620, Republic of KoreaWe construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters.https://www.mdpi.com/2075-1680/12/5/452domain decomposition methodsoverlapping Schwarz methodsbiharmonic problemseffective preconditionersisogeometric analysisgeneralized B-splines |
| spellingShingle | Durkbin Cho Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem Axioms domain decomposition methods overlapping Schwarz methods biharmonic problems effective preconditioners isogeometric analysis generalized B-splines |
| title | Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem |
| title_full | Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem |
| title_fullStr | Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem |
| title_full_unstemmed | Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem |
| title_short | Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem |
| title_sort | isogeometric schwarz preconditioners with generalized b splines for the biharmonic problem |
| topic | domain decomposition methods overlapping Schwarz methods biharmonic problems effective preconditioners isogeometric analysis generalized B-splines |
| url | https://www.mdpi.com/2075-1680/12/5/452 |
| work_keys_str_mv | AT durkbincho isogeometricschwarzpreconditionerswithgeneralizedbsplinesforthebiharmonicproblem |