Obtaining smooth mesh transitions using vertex optimization

Mesh optimization has proven to be an effective way to improve mesh quality for arbitrary Lagrangian Eulerian (ALE) simulations. To date, however, most of the focus has been on improving the geometric shape of individual elements, and these methods often do not result in smooth transitions in element size or aspect ratio across groups of elements. We present an extension to the mean ratio optimization that addresses this problem and yields smooth transitions within regions and across regions in the ALE simulation. While this method is presented in the context of ALE simulations, it is applicable to a wider set of applications that require mesh improvement, including the mesh generation process. Published in 2007 by John Wiley & Sons, Ltd.