Automatic Mesh Generation on a Regular Background Grid

This paper presents an automatic mesh generation procedure on a 2Ddomain based on a regular background grid. The idea is to devise arobust mesh generation scheme with equal emphasis on quality andefficiency. Instead of using a traditional regular rectangular grid, amesh of equilateral triangles is employed to ensure triangular elementof 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 insertionprocess. Nodes are inserted into the background mesh one by onefollowing the sequence of the domain boundary. The local structure ofthe mesh is modified based on the Delaunay criterion with theintroduction of each node. Those boundary segments, which are notproduced in the phase of node insertion, will be recovered through asystematic element swap process. Two theorems will be presented andproved to set up the theoretical basic of the boundary recovery part.Examples will be presented to demonstrate the robustness and thequality of the mesh generated by the proposed technique.