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A method for hexahedral mesh shape optimization
Author(s) -
Knupp Patrick M.
Publication year - 2003
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.768
Subject(s) - hexahedron , polygon mesh , jacobian matrix and determinant , computer science , robustness (evolution) , laplacian smoothing , mathematical optimization , metric (unit) , laplace operator , smoothing , mesh generation , finite element method , algorithm , mathematics , engineering , structural engineering , mathematical analysis , biochemistry , chemistry , operations management , computer graphics (images) , computer vision , gene
Methods for improving the quality of all‐hexahedral unstructured meshes by node‐movement strategies have, until recently, been lacking. Laplacian smoothing, while easily implemented and well‐known, fails to guarantee improvement of mesh quality and may result in inverted elements where none existed before. A method for improving unstructured hexahedral mesh shape‐quality that guarantees untangled elements is proposed. The method is based on optimization of an objective function built from the quality of individual hexahedral elements. The shape‐quality measure for hexahedral elements is based on the condition number of a set of Jacobian metrics associated with the element. The theory of the condition number quality metric and of the objective function are reviewed. A numerical optimization procedure to find the improved‐quality mesh is described. The purpose of this paper is to demonstrate the robustness of the method. We do so by giving a realistic example. The method has also been successfully applied to dozens of meshes on complex geometries. Published in 2003 by John Wiley & Sons, Ltd.

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