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...
| Autores: | , , , |
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| 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 |
| 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. |
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