Stability Aware Delaunay Refinement

Abstract

Good quality meshes are extensively used for finding approximate solutions for partial differential equations for fluid flow in two dimensional surfaces. We present an overview of existing algorithms for refinement and generation of triangular meshes. We introduce the concept of node stability in the refinement of Delaunay triangulation. We present an algorithm based on the location of center of gravity of two dimensional shapes to place a candidate refinement node so that the newly placed node has increased stability. The algorithm runs in O(n2) time, where n is the number of nodes in the mesh.