Optimization of a regularized distortion measure to generate curved high-order unstructured tetrahedral meshes

We present a robust method for generating high-order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second, displacing the boundary nodes to ensure that they are on the CAD surface, and third, smoothing and untanglin...

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Detalles Bibliográficos
Autores: Gargallo Peiró, Abel|||0000-0003-3742-2197, Roca Navarro, Francisco Javier, Peraire Guitart, Jaume, Sarrate Ramos, Josep|||0000-0003-0182-934X
Tipo de recurso: artículo
Fecha de publicación:2015
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:2117/76950
Acceso en línea:https://hdl.handle.net/2117/76950
https://dx.doi.org/10.1002/nme.4888
Access Level:acceso abierto
Palabra clave:Operations research
unstructured high-order methods
mesh generation
CAD
mesh optimization
mesh quality
curved meshing
Investigació operativa
Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
Descripción
Sumario:We present a robust method for generating high-order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second, displacing the boundary nodes to ensure that they are on the CAD surface, and third, smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high-order mesh. The smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh. This means that whenever possible, the resulting mesh preserves the geometrical features of the initial linear mesh such as shape, stretching and size. We present several examples to illustrate the performance of the proposed algorithm. Furthermore, the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements. The meshes obtained are suitable for high-order finite element analyses.