Some of my go to references.

Research

James Hall

Postdoctoral Scholar

University of California, San Diego

Office: APM 5824

Email: j9hall@math.ucsd.edu

Computational Geometric Mechanics

My research focuses on improving simulations of physical systems. I develop highly accurate and efficient numerical methods that make use of the geometric structure of physical systems.

High Order Galerkin Variational Integrators

High Order Galerkin Variational Integrators are highly accurate numerical methods that make use of the structure of a mechanical system. The advantage they have over classical methods is that they are stable at very long time steps and for very long periods of time.

For example, if you try to get MATLAB's built-in ODE solvers to simulate the Solar System 1000 years into the future, this is the result you get:

Lie Group Galerkin Variational Integrators

Efficient Implementation of Galerkin Variational Integrators

Automated Wound Sizing

I am currently working on developing methods for automatically measuring the size of wounds from photographs. This project is being done in collaboration with Katherine Walsh from UCSD Mathematics and Dr. Nicole Gaid from the UCSD medical school.

Automated Pattern Recognition

My master's thesis focused on developing methods of texture recognition.

Other Projects

During my early years as a PhD students, and as a master's student, I worked on a number of projects.