Deflation-based preconditioning for immersed finite element methods and immersogeometric analysis
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908964023697408 |
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| author | Voet, Yannis Möller, Matthias Antolin, Pablo Vuik, Cornelis |
| author_facet | Voet, Yannis Möller, Matthias Antolin, Pablo Vuik, Cornelis |
| contents | Trimming is a ubiquitous operation in computer-aided-design whereby parts of a geometry are merged, intersected, or simply discarded. While it grants virtually unlimited flexibility in geometric design, it introduces a plethora of other difficulties when such geometries are used within immersed finite element methods. In particular, small cut elements lead to severely ill-conditioned system matrices requiring dedicated penalization, stabilization, or preconditioning techniques. In this work, we highlight the limitations of existing preconditioning strategies by first carefully examining the condition number of the diagonally scaled matrix and later providing realistic counter-examples for some well-established preconditioning strategies. Building on those insights, we propose a robust deflation-based preconditioning technique tailored to immersed finite element methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12848 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deflation-based preconditioning for immersed finite element methods and immersogeometric analysis Voet, Yannis Möller, Matthias Antolin, Pablo Vuik, Cornelis Numerical Analysis 65F08, 65F10, 65M60, 65N30 Trimming is a ubiquitous operation in computer-aided-design whereby parts of a geometry are merged, intersected, or simply discarded. While it grants virtually unlimited flexibility in geometric design, it introduces a plethora of other difficulties when such geometries are used within immersed finite element methods. In particular, small cut elements lead to severely ill-conditioned system matrices requiring dedicated penalization, stabilization, or preconditioning techniques. In this work, we highlight the limitations of existing preconditioning strategies by first carefully examining the condition number of the diagonally scaled matrix and later providing realistic counter-examples for some well-established preconditioning strategies. Building on those insights, we propose a robust deflation-based preconditioning technique tailored to immersed finite element methods. |
| title | Deflation-based preconditioning for immersed finite element methods and immersogeometric analysis |
| topic | Numerical Analysis 65F08, 65F10, 65M60, 65N30 |
| url | https://arxiv.org/abs/2604.12848 |