An Isogeometric Tearing and Interconnecting method for conforming discretizations of the biharmonic problem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908635992424448 |
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| author | Takacs, Stefan |
| author_facet | Takacs, Stefan |
| contents | We propose and analyze a domain decomposition solver for the biharmonic problem. The problem is discretized in a conforming way using multi-patch Isogeometric Analysis. As first step, we discuss the setup of a sufficiently smooth discretization space. We focus on two dimensional computational domains that are parameterized with sufficiently smooth geometry functions. As solution technique, we use a variant of the Dual-Primal Finite Element Tearing and Interconnecting method that is also known as Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method in the context of Isogeometric Analysis. We present a condition number estimate and illustrate the behavior of the proposed method with numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Isogeometric Tearing and Interconnecting method for conforming discretizations of the biharmonic problem Takacs, Stefan Numerical Analysis 65N55, 65N30, 65F08, 65D07 We propose and analyze a domain decomposition solver for the biharmonic problem. The problem is discretized in a conforming way using multi-patch Isogeometric Analysis. As first step, we discuss the setup of a sufficiently smooth discretization space. We focus on two dimensional computational domains that are parameterized with sufficiently smooth geometry functions. As solution technique, we use a variant of the Dual-Primal Finite Element Tearing and Interconnecting method that is also known as Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method in the context of Isogeometric Analysis. We present a condition number estimate and illustrate the behavior of the proposed method with numerical results. |
| title | An Isogeometric Tearing and Interconnecting method for conforming discretizations of the biharmonic problem |
| topic | Numerical Analysis 65N55, 65N30, 65F08, 65D07 |
| url | https://arxiv.org/abs/2511.05247 |