2026-04-05T10:45:32Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/3830192026-02-09T07:22:05Zcom_2072_1033col_2072_452950

Conformal marked bisection for local refinement of n-dimensional unstructured conformal meshes Belda Ferrín, Guillem Ruiz Gironès, Eloi Roca Navarro, Francisco Javier Gargallo Peiró, Abel Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Difference equations--Numerical solutions unstructured conformal mesh adaption mesh refinement local bisection n-dimensional bisection Equacions diferencials--solucions numèriques Classificació AMS::65 Numerical analysis::65L Ordinary differential equations We present an n-dimensional marked bisection method for unstructured conformal meshes. We devise the method for local refinement in adaptive n-dimensional applications. To this end, we propose a mesh marking pre-process and three marked bisection stages. The pre-process marks the initial mesh conformingly. Then, in the first n-1 bisections, the method accumulates in reverse order a list of new vertices. In the second stage, the n-th bisection, the method uses the reversed list to cast the bisected simplices as reflected simplices, a simplex type suitable for newest vertex bisection. In the final stage, beyond the n-th bisection, the method switches to newest vertex bisection. To allow this switch, after the second stage, we check that under uniform bisection the mesh simplices are conformal and reflected. These conditions are sufficient to use newest vertex bisection, a bisection scheme guaranteeing key advantages for local refinement. Finally, the results show that the proposed bisection is well-suited for local refinement of unstructured conformal meshes. Peer Reviewed Postprint (author's final draft) 2023-01-01 Article https://www.sciencedirect.com/science/article/pii/S001044852200152X info:eu-repo/grantAgreement/EC/H2020/715546/EU/Best Curved Adapted Meshes for Space-Time Flow Simulations/Tesseract http://creativecommons.org/licenses/by/4.0/ Open Access Attribution 4.0 International Elsevier