Tetrahedral Mesh Optimization and Generation via Topological Transformation and Gradient Based Node Perturbation

A Dissertation Presented for the Doctor of Philosophy in Computational Engineering, The University of Tennessee at Chattanooga

C. Bruce Hilbert, August 2015


A general tetrahedral mesh optimization scheme utilizing both topological changes (i.e. flips) and gradient-based vertex optimization (i.e. smoothing) is demonstrated. This scheme is used in the optimization of tetrahedral meshes created by third-party software as well as a grid generation methodology created for this work. The particular algorithms involved are explained in detail including, an explication of the primary optimization metric, weighted condition number. In addition, a thorough literature review regarding tetrahedral mesh generation is given.

Bruce Hilbert Doctoral Dissertation

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