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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.14063 |
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| _version_ | 1866908371462914048 |
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| author | Berrone, Stefano Borio, Andrea Teora, Gioana Vicini, Fabio |
| author_facet | Berrone, Stefano Borio, Andrea Teora, Gioana Vicini, Fabio |
| contents | This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support advanced numerical techniques, with a focus on the Virtual Element Method in both 2D and 3D settings. PolyDiM is designed to address a wide range of challenging problems, including those involving non-convex geometries, Discrete Fracture Networks, and mixed-dimensional coupling. It is integrated with the geometry library GeDiM, and offers interfaces for MATLAB and Python to enhance accessibility. Distinguishing features include support for multiple polynomial bases, advanced stabilization strategies, and efficient local-to-global assembly procedures. PolyDiM aims to serve both as a research tool and a foundation for scalable scientific computing in complex geometrical settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | POLYDIM: A C++ library for POLYtopal DIscretization Methods Berrone, Stefano Borio, Andrea Teora, Gioana Vicini, Fabio Numerical Analysis 65M60 G.1.8; G.1.4; D.3.0 This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support advanced numerical techniques, with a focus on the Virtual Element Method in both 2D and 3D settings. PolyDiM is designed to address a wide range of challenging problems, including those involving non-convex geometries, Discrete Fracture Networks, and mixed-dimensional coupling. It is integrated with the geometry library GeDiM, and offers interfaces for MATLAB and Python to enhance accessibility. Distinguishing features include support for multiple polynomial bases, advanced stabilization strategies, and efficient local-to-global assembly procedures. PolyDiM aims to serve both as a research tool and a foundation for scalable scientific computing in complex geometrical settings. |
| title | POLYDIM: A C++ library for POLYtopal DIscretization Methods |
| topic | Numerical Analysis 65M60 G.1.8; G.1.4; D.3.0 |
| url | https://arxiv.org/abs/2505.14063 |