Over the summer of 2017, I worked on simulating MHD using discrete exterior calculus. Following this paper by Kraus and Maj, I implemented a 2D MHD simulation in periodic domains. I then proved that the method conserves energy and cross-helicity, and I extended the method to domains with boundaries.

Below are some results of the simulation. The magnetic field strength is visualized by a glowing effect. You can see the fluid carrying the magnetic field upwards, where it collides with the container's boundary and starts to flow sideways.

I implemented the algorithm in HoudiniFX, and used Houdini to render these images.

In the winter of 2016, I implemented a variational integrator for multiple pendula as a final project for a graphics class. I used the method of Marsden and West described here (also available here) to simulate a physical system with constraints.

Here are some interesting assignments that I implemented for a discrete differential geometry class in the fall of 2016.

I computed the normal modes of the discrete Laplacian on the Stanford bunny. Here are the first 4.

Using these normal modes, I numerically solved a Poisson equation to find the electric field induced by charges on the bunny's surface.

Recently, I've been working with Professor Alan Barr on using Interval Analysis to solve root-finding and minimization problems. Interval analysis is the technique of doing computations with intervals representing uncertainty instead of regular real numbers. This provided guaranteed bounds on the accuracy of your results. Our code is available on GitHub.