I am currently a PhD Candidate at the University of North Carolina at Greensboro. I attended Mars Hill University (though, it will always be Mars Hill College to me) for my B.S. in Mathematics and Western Carolina University for my M.S. in Applied Mathematics. The reserach that I completed for my M.S. at Western Carolina University was mentored by Dr. Mark Budden in the field of Ramesy Theory and Hypergraphs. While at UNCG I decided to instead complete research in numerical methods on partial differential equations. The current title of my dissertation is "Convergence analysis of symmetric dual-wind discontinuous Galerkin methods for the obstacle problem." Outside of academia I do Crossfit, play volleyball, soccer, kickball, and quidditch. (Yes, quidditch. Here is a link to the United States Quidditch Organization.)
Univeristy of North Carolina at Greensboro
Western Carolina University
Mars Hill University
University of North Carolina at Greensboro
University of North Carolina at Greensboro
University of North Carolina at Greensboro
University of North Carolina at Greensboro
Western Carolina University
Western Carolina University
Western Carolina University
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The Obstacle Problem
The obstacle problem is a variational inequality that finds the equilibrium position of an elastic membrane that passes through the boundary of an open set, that is subjected to a force of density, and lies over an obstacle. A basic summary of the obstacle problem can be found here paper. The image to the left is the solution of the obstacle problem (in this case, the obstacle function is f(x,y)=0).
The DWDG Methods
The dual-wind discontinuous Galerkin (DWDG) methods are a class of discontinuous Galerkin (DG) methods that are formed from DG derivatives that can be found in this paper. The DWDG methods are a class of DG methods that can be penalty-free. This is a big benefit for industrial applications. In my dissertation, I have been able to prove that this method has optimal convergence rates with low regularity of the true solution. The movie to the left is the penalty-less DWDG approximation to the solution given in the image above.
Submitted, July 2019
Hypergraph Ramsey Numbers Involving Paths
Acta Universitatis Apulensis, Vol 48, pg 75-87 (2016)
Generalized Ramsey theorems for r-uniform hypergraphs
The Australasian Journal of Combinatorics, Vol 63, pg 142-152 (2015)
Constructing r-Uniform Hypergraphs with Restricted Clique Numbers
The North Carolina Journal of Mathematics and Statistics, Vol 1, pg 30-34 (2015)
A lifiting of graphs to 3-uniform hypergraphs, its generalization, and further investigation of hypergraph ramsey numbers
Western Carolina University, Master's Thesis (2015)
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