New approaches for Delaunay triangulation and optimisation

Abstract

New techniques are presented for Delaunay triangular mesh generation and element optimisation. Sample points for triangulation are generated through mapping (a new approach). These sample points are later triangulated by the conventional Delaunay method. Resulting triangular elements are optimised by addition, removal and relocation of mapped sample points (element nodes). The proposed techniques (generation of sample points through mapping for Delaunay triangulation and mesh optimisation) are demonstrated by using Mathematica software. Simulation results show that the proposed techniques are able to form meshes that consist of triangular elements with aspect ratio of less than 2 and minimum skewness of more than 45°.

Keywords

• Mechanical engineering
• Finite element methods
• Mathematical modeling
• Geometry
• Computing methodology
• Computer simulation