Publication Date

12-2013

Date of Final Oral Examination (Defense)

8-2-2013

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Donna Calhoun, Ph.D.

Supervisory Committee Member

Jodi Mead, Ph.D.

Supervisory Committee Member

Grady Wright, Ph.D.

Abstract

This thesis describes a new approach to computing mean curvature and mean curvature normals on smooth logically Cartesian surface meshes. We begin by deriving a finite-volume formula for one-dimensional curves embedded in two- or three- dimensional space. We show the exact results on curves for specific cases as well as second-order convergence in numerical experiments. We extend this finite-volume formula to surfaces embedded in three-dimensional space. Exact results are again derived for special cases and second-order convergence is shown numerically for more general cases. We show that our formula for computing curvature is an improvement over using the “cotan” formula on a triangulated quadrilateral mesh and is conceptually much simpler than the formula proposed by Liu et al. (“A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes”, Computers and Mathematics with Applications, 2008), and is equivalent in performance.

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