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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.05124 |
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| _version_ | 1866911334095912960 |
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| author | Pitassi, Silvano |
| author_facet | Pitassi, Silvano |
| contents | Given a compact surface $Γ$ embedded in $\mathbb R^3$ with boundary $\partial Γ$, our goal is to construct a set of representatives for a basis of the relative cohomology group $H^1(Γ, \partial Γ^c)$, where $Γ^c$ is a specified subset of $\partial Γ$. To achieve this, we propose a novel graph-based algorithm with two key features: it is applicable to non-orientable surfaces, thereby generalizing the construction of Hiptmair and Ostrowski [SIAM J. Comput., 31 (2002)], and it has a worst-case time complexity that is linear in the number of edges of the mesh $\mathcal K$ triangulating $Γ$. Importantly, this algorithm serves as a critical pre-processing step to address the low-frequency breakdown encountered in boundary element discretizations of integral equation formulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generators of $H^1(Γ, \partial Γ^c)$ with $\partial Γ^c \subset \partial Γ$ for Triangulated Surfaces $Γ$: Construction and Classification of Global Loops Pitassi, Silvano Numerical Analysis Given a compact surface $Γ$ embedded in $\mathbb R^3$ with boundary $\partial Γ$, our goal is to construct a set of representatives for a basis of the relative cohomology group $H^1(Γ, \partial Γ^c)$, where $Γ^c$ is a specified subset of $\partial Γ$. To achieve this, we propose a novel graph-based algorithm with two key features: it is applicable to non-orientable surfaces, thereby generalizing the construction of Hiptmair and Ostrowski [SIAM J. Comput., 31 (2002)], and it has a worst-case time complexity that is linear in the number of edges of the mesh $\mathcal K$ triangulating $Γ$. Importantly, this algorithm serves as a critical pre-processing step to address the low-frequency breakdown encountered in boundary element discretizations of integral equation formulations. |
| title | Generators of $H^1(Γ, \partial Γ^c)$ with $\partial Γ^c \subset \partial Γ$ for Triangulated Surfaces $Γ$: Construction and Classification of Global Loops |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.05124 |