Conformal marked bisection for local refinement of n-dimensional unstructured conformal meshes

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 confor...

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Detalles Bibliográficos
Autores: Belda Ferrín, Guillem|||0000-0002-6268-7691, Ruiz Gironès, Eloi, Roca Navarro, Francisco Javier, Gargallo Peiró, Abel|||0000-0003-3742-2197
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/383019
Acceso en línea:https://hdl.handle.net/2117/383019
https://dx.doi.org/10.1016/j.cad.2022.103419
Access Level:acceso abierto
Palabra clave: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
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Descripción
Sumario: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.