Fully Anisotropic Split-Tree Adaptive Refinement Mesh Generation Using Tetrahedral Mesh Stitching

Abstract

This dissertation is dedicated to Cassandra Betro, my loving wife, who has seen me through the process of starting a family while getting my Doctoral Degree and loved me through all the difficulties life has presented. It is also dedicated to Savannah Betro-Gross, my step-daughter, who has taught me to love unconditionally through everything, because she is the kindest, best person I have ever met. I also dedicate this to my family and friends, who have given so much support through life changes, and to my colleagues, especially Dr. Steve Karman, who have helped me grow as an engineer, educator, and person. I thank God for giving me this opportunity and giving me the support I needed to make it through. Finally, I dedicate this dissertation to Vincent Moses Betro, who should be along shortly, for giving me a deadline...I cannot wait to meet you, my son! iii

Advances in Parallelization For Large Scale Oct-Tree Mesh Generation

“…Other parallel meshing techniques also generate base meshes down to a user desired maximum depth; however, these techniques enforce quality rules in the base mesh. 4,8 These techniques can be described as top down methods since they begin at the top of the tree and generate the mesh as they traverse down. The technique proposed here differs from those methods by generating only the smallest possible tree structure that contains pieces of the geometry.…”

“…Other techniques, such as Hexagrid, project nodes from the off-body mesh onto the geometry. 7 FASTAR 8 was developed using a type of binary tree called a split-tree. It uses tetrahedral meshing to combine a hierarchical technique for off-body grids to a body conforming viscous mesh generated using extrusion.…”

“…3 Rather than use a strictly top down or bottom up method, Betro introduced a hybrid method that begins as a top down approach and finishes as bottom up. 8 That work was done using a specialized binary tree called a split tree. In recent years a number of researchers have developed dynamically load balanced parallel oct-tree methods.…”