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Optimization of a regularized distortion measure to generate curved high‐order unstructured tetrahedral meshes
Author(s) -
GargalloPeiró A.,
Roca X.,
Peraire J.,
Sarrate J.
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4888
Subject(s) - polygon mesh , smoothing , boundary (topology) , tetrahedron , distortion (music) , measure (data warehouse) , mesh generation , laplacian smoothing , volume mesh , finite element method , mathematics , algorithm , computer science , mathematical optimization , geometry , topology (electrical circuits) , mathematical analysis , structural engineering , combinatorics , engineering , amplifier , computer network , statistics , bandwidth (computing) , database
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.