Résumé
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.