Aspects of the implementation of two-dimensional mesh generation algorithm

Abstract

Delaunay refinement is a technique for generating unstructured meshes of triangles to be used in the finite element method. In theory and practice, meshes produced by Delaunay refinement satisfy guaranteed bounds on angles, edge lengths, the number of triangles, and the grading of triangles from small to large sizes. This article presents a few notes about the implementation of L. Paul Chew and Jim Ruppert's mesh generation algorithm. The most valuable innovation presented is an incremental triangulation algorithm which runs in O(n) time and naturally embeds in Delaunay refinement algorithm given by Jim Ruppert. There are also some innovations in the data structures, locating of triangles and the elimination of triangles, which are out of the problem domain boundary.