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

Summary 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 computer‐aided design surface, and thir...

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Vydáno v:International journal for numerical methods in engineering Ročník 103; číslo 5; s. 342 - 363
Hlavní autoři: Gargallo-Peiró, A., Roca, X., Peraire, J., Sarrate, J.
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Bognor Regis Blackwell Publishing Ltd 03.08.2015
Wiley Subscription Services, Inc
Témata:
90 Operations research, mathematical programming
90B Operations research and management science
Algorithms
Boundaries
CAD
Classificació AMS
Curved
curved meshing
Displacement
Distortion
Investigació operativa
Matemàtiques i estadística
mesh generation
mesh optimization
mesh quality
Operations research
Optimització
Optimization
Preserves
Smoothing
unstructured high-order methods
Àrees temàtiques de la UPC
ISSN:0029-5981, 1097-0207, 1097-0207
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Shrnutí:Summary 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 computer‐aided design 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. Copyright © 2015 John Wiley & Sons, Ltd.
Bibliografie:ark:/67375/WNG-XPQL77BZ-Z
ArticleID:NME4888
istex:1C7241A4F15A23BF187A8BFB0C06B4C8B512F464
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.4888