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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.05124 |
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Table of 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.