Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917011389415424 |
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| author | Adjerid, Slimane Lin, Tao Meghaichi, Haroun |
| author_facet | Adjerid, Slimane Lin, Tao Meghaichi, Haroun |
| contents | The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a procedure for constructing the local IFE bases in some detail as well as a new approach for constructing orthonormal bases using the singular value decomposition of the local generalized Vandermonde matrix. A sample implementation in MATLAB is provided to showcase the simplicity and extensionability of the framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method Adjerid, Slimane Lin, Tao Meghaichi, Haroun Numerical Analysis 65N30 G.1.8 The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a procedure for constructing the local IFE bases in some detail as well as a new approach for constructing orthonormal bases using the singular value decomposition of the local generalized Vandermonde matrix. A sample implementation in MATLAB is provided to showcase the simplicity and extensionability of the framework. |
| title | Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method |
| topic | Numerical Analysis 65N30 G.1.8 |
| url | https://arxiv.org/abs/2510.12018 |