Award Date

8-1-2013

Degree Type

Thesis

Degree Name

Master of Science in Computer Science

Department

Computer Science

First Committee Member

Laxmi Gewali

Second Committee Member

John Minor

Third Committee Member

Evangelos Yfantis

Fourth Committee Member

Rama Venkat

Number of Pages

64

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 two algorithms for generating stable refinement of Delaunay triangulation. We also present an experimental investigation of a triangulation refinement algorithm based on the location of the center of gravity and the location of the center of circumcircle. The results show that the center of gravity based refinement is more effective in refining interior nodes for a given distribution of nodes in two dimensions.

Keywords

Algorithms; Delaunay refinement; Delaunay triangulation; Differential equations, Partial – Numerical solutions; Mesh refinement; Reliable mesh refinement; Stable mesh refinement; Triangulation; Triangulation refinement

Disciplines

Computer Sciences | Partial Differential Equations

Language

English


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