Pré-Publication, Document De Travail Année : 2025

Generators of $H^1(\Gamma, \partial \Gamma^c)$ with $\partial \Gamma^c \subset \partial \Gamma$ for Triangulated Surfaces $\Gamma$: Construction and Classification of Global Loops

Résumé

Given a compact surface $\Gamma$ embedded in $\mathbb{R}^3$ with boundary $\partial \Gamma$, our goal is to construct a set of representatives for a basis of the relative cohomology group $H^1(\Gamma, \partial \Gamma^c)$, where $\Gamma^c$ is a specified subset of $\partial \Gamma$. To achieve this, we propose a novel graph-based algorithm with two key features: it is applicable to non-orientable surfaces, thereby generalizing previous approaches, and it has a worst-case time complexity that is linear in the number of edges of the mesh $\mathcal{K}$ triangulating $\Gamma$. 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.
Fichier principal
Vignette du fichier
loop-star.pdf (538.41 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
licence

Dates et versions

hal-04876473 , version 1 (09-01-2025)

Licence

Identifiants

  • HAL Id : hal-04876473 , version 1

Citer

Silvano Pitassi. Generators of $H^1(\Gamma, \partial \Gamma^c)$ with $\partial \Gamma^c \subset \partial \Gamma$ for Triangulated Surfaces $\Gamma$: Construction and Classification of Global Loops. 2025. ⟨hal-04876473⟩
0 Consultations
0 Téléchargements

Partager

More