Distortion measure of trilinear mapping. Application to 3‐D grid generation

Abstract

Abstract Distortion measures for polylinear mappings are investigated. It is shown that certain distortion measures satisfy the maximum principle which allows us to obtain upper bounds on the distortion measures for hexahedral cells and other types of elements widely used in the finite element method. These estimates allow to apply a maximum‐norm optimization technique for spatial mappings in the case of finite element grids consisting of hexahedra. A global hexahedral grid untangling procedure suggested earlier was tested on hard 3‐D examples demonstrating its ability to work in a black box mode and its high level of robustness. Copyright © 2002 John Wiley & Sons, Ltd.