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Finite Element Methods on GPU Coprocessors

Research 2008-2009. Coming Soon.

Fourier Based Fast Multipole Method for the Helmholtz Equation

Research 2007-2008. Coming Soon.

Abstract Art Generator

I wrote this program one lonely day over a winter break. It simply generates random functions. I had a good time optimizing the crap out of it so that good things can happen in reasonable amounts of time.

Thomson Problem

I began to write this program in the summer of 2004 when I was hired as a research assistant in Condensed Matter Physics at Syracuse University under Professor Alan Middleton, Professor Mark Bowick, and Professor Cristina Marchetti. I would return to Syracuse over winter break of 2004 and went back for half of summer 2005 to consult with Professor Alex Travesset and continue development.

I ran into a number of interesting problems:

• Writing and streamlining a fast graphics engine.
• Learning computational geometry and deriving a lightning fast Delaunay triangulation algorithm over spherical and toroidal topology.

The applet now houses the largest and most interactive database on the Thomson problem and related systems.

Vascular Tumor Modeling

This project was my undergraduate senior clinic project, which is similar to a thesis. Over the course of the year, I worked on a team with 4 Harvey Mudd seniors - Alan Davidson (CS), Tiffany Head (Math), Dana Mohamed (Math-Bio), and Liam Robinson (Math) - in conjunction with Los Alamos National Laboratory to vascularize an existing multiscale tumor model. The model was composed of

• Extracellular Model - Diffusion of chemicals between cells.
• Cellular Model - Monte Carlo governed cell movement and growth.
• Subcellular Model - Cell cycle, protein network, and protein expression.

We investigated the effects of a vasculature on tumor growth as well as the impacts of various chemotherapy models. The final report may be accessed from the link above.

Primarily, I researched and wrote a diffusion equation integrator with time and space dependent source/sink terms which could be applied to a system with arbitrary Dirichlet boundary condition geometries. The integrator was composed of a backward Euler approximation with an adaptive Gauss-Seidel iteration.

• A short presentation poster.
• The final presentation to HMC and Los Alamos.

Quantum Applet

A final project for an undergraduate Computational Physics course that extended a previous project which only used a custom numerical integrator. This version uses a spectral algorithm and has numerous updates to the GUI.

Quantum Computing Research

Linked above is a short summary of some of the research into Quantum Computing and Quantum Information I conducted with Professor Chris Stone over the summer of 2005. During that summer, we

• researched and developed a framework for quantum computing languages,
• determined the requirements and restrictions of any quantum computing language (quantum operator and quantum bit manipulation, reversibility, state coherence, no cloning, etc),
• researched current quantum computing algorithms and worked on improvement, optimization, and correctness of these algorithms (Deutsch-Jozsa, Grover, Shor, teleportation, encryption, operator decomposition, etc),
• implemented some of these algorithms in various existing quantum computing languages and simulators including QCL and Q-Language and also implemented small improvements to those languages.

A presentation I gave on Grover's algorithm.

ICM Competition

I participated in the 2006 Interdisciplinary Contest in Modeling (ICM) with Tristan Sharp (Physics) and Michael Martin (Physics). The ICM is a 96-hour competition where teams tackle complex problems for which they must formulate, describe, apply, and analyze a mathematical model in a comprehensive final report. It is designed to develop and advance interdisciplinary problem-solving skills as well as competence in written communication.

Our paper, AIDS: Modeling a Global Crisis (and Australia), was recognized as one of the top four outstanding papers in a pool of 225 participating teams and was selected for publication in The UMAP Journal 27.2. The paper describes a mathematical model for the spread of HIV, the future economic impact of treating HIV under preventative, retroactive, and proactive treatments, and the impact of these models under the emergence of resistive strains of HIV. The model was applied to 6 countries around the world using current UNAIDS data and analyzed for accuracy and predictive strength.

• The most ridiculus problem statement for a 96-hour project ever.
• The submitted final paper and the compressed, published version in The UMAP Journal

Connect Four

An indepedent project which was based on a freshman year introduction level CS course assignment.

Gravitational N-Body

A midterm project for an undergraduate Computational Physics course. Extending on the assignment, my goal was to make a general N-Body integrator based on a simple Runge-Kutta iteration (successful) and to package it in a relatively nice GUI (semi-successful). The final report for this project uses the model in a Fourier analysis of a planet within the Alpha-Centari binary star system.

DESC

Double Ended Spam Cruncher. A simple, but entertaining, applet which I extended from a mid-level undergraduate CS course.