Automatic mesh generation on a regular background grid

Abstract

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.