Delaunay Refinement Mesh Generation.

摘要

Delaunay refinement is a technique for generating unstructured meshes of triangles or tetrahedral suitable for use in the finite element method or other numerical methods for solving partial differential equations. Popularized by the engineering community in the mid-1980s, Delaunay refinement operates by maintaining a Delaunay triangulation or Delaunay tetrahedralization, which is refined by the insertion of additional vertices. The placement of these vertices is chosen to enforce boundary conformity and to improve the quality of the mesh. Pioneering papers by L. Paul Chew and Jim Ruppert have placed Delaunay refinement on firm theoretical ground. The purpose of this thesis is to further this progress by cementing the foundations of two- dimensional Delaunay refinement, and by extending the technique and its analysis to three dimensions.