2026-04-13T01:49:08Zhttps://recercat.cat/oai/request

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

00925njm 22002777a 4500 dc Belda Ferrín, Guillem author Ruiz Gironès, Eloi author Roca Navarro, Francisco Javier author Gargallo Peiró, Abel author 2023-01-01 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) 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 Conformal marked bisection for local refinement of n-dimensional unstructured conformal meshes