A method for hexahedral mesh shape optimization

International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 58, Num 2, pp.319-332, July 2003

MESHING
RESEARCH
CORNER

Abstract

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.