Automatic mesh generation on a regular background grid

This paper presents an automatic mesh generation procedure on a 2D domain based on a regular background grid. The idea is to devise a robust mesh generation scheme with equal emphasis on quality and efficiency. Instead of using a traditional regular rectangular grid, a mesh of equilateral triangles is employed to ensure triangular element of the best quality will be preserved in the interior of the domain. As for the boundary, it is to be generated by a node/segment insertion process. Nodes are inserted into the background mesh one by one following the sequence of the domain boundary. The local structure of the mesh is modified based on the Delaunay criterion with the introduction of each node. Those boundary segments, which are not produced in the phase of node insertion, will be recovered through a systematic element swap process. Two theorems will be presented and proved to set up the theoretical basic of the boundary recovery part. Examples will be presented to demonstrate the robustness and the quality of the mesh generated by the proposed technique. Supported by the University Grant Councill (UGC) for the project “Analysis of building structure using hybrid stress hexahedral elements”. LO S. H. graduated from the Department of Civil and Structural Engineering at the University of Hong Kong in 1979. He obtained the M.Ph. degree from the same department in 1985. He finished his Docteur-Ingenieur degree at Ecole des Ponts et Chaussees, Paris, in 1986. After working two years for P.S.A. Automobile Group in France, S. H. Lo went back to Hong Kong and joined the Department as a lecturer in 1988, and was promoted to senior lecturer in 1994. His research interests include the finite element method, adaptive refinement analysis, computer graphics in engineering applications, large deformation problems, etc. He is a co-editor of the section “Structural analysis and CAD” for the journal “Progress in Structural Engineering and Materials”, and he is also a member of the editorial board of the international journal “Finite Elements in Analysis and Design”. He was a visiting professor to INRIA, France in 1994 and 1998. LIU Jianfei received his Ph.D. degree from the Beijing University of Aeronautics and Astronautics in 1991. He is an associate professor of Peking University. His research interests include mesh generation and computer aided design.