CONTACT INFORMATION:

Adam Wermus | wermusam@dukes.jmu.edu | 757-333-2488

Hello and welcome! My background is in Math and Physics and my research is on optimizing physical simulations in animation. I focus on different numerical methods that solve the equations of motion of a simulation to see what advantages and disadvantages the different methods have.

A lot of focus is on The Parker-Sochacki Method, which is a relatively new technique developed by my professors at James Madison University. To my knowledge this is the only place where it is being tested in the field of computer graphics. It is a power series method that converts a system of First Order Initial Value Ordinary Differential Equations into a Maclaurin series up to any order. I’ve been researching how Parker-Sochaki performs at different orders, finding more applications, and studying ways to improve it.

I’m also studying ways to improve other numerical integratoion methods by combining them with methods like Pade and Laplace-Pade. This research is ongoing but because Pade and Laplace-Pade expand the domain of convergence, I’m combining this with different Euler methods, Verlet methods, Runge-Kutta methods, Generalized-Alpha, and BDF2.

Below are videos that compare different methods in terms of flexibility, conservation of energy, and time step size.

**VIDEOS THAT COMPARE EXPLICIT EULER, SEMI-IMPLICIT EULER, IMPLICIT EULER, VELOCITY VERLET, RUNGE-KUTTA 2ND ORDER MIDPOINT, RUNGE-KUTTA 4TH ORDER, AND PARKER-SOCHACKI AT VARIOUS ORDERS
**

Flexibility of Springs | Conservation of Energy on a Pendulum | 3-Body Largest Possible Time Step |

Energy Conservation after Collisions 1 | Energy Conservation after Collisions 2 |

To see a mathematical step by step for Parker-Sochacki, code, and more animations of a simulation, click on one of the sections above. I also have section for Stereoscopy where I created 3D images of a cornet, Motion Capture where I replicated a form from the James Madison University Tae Kwon Do Club, and a Trumpet Research section where I created a 3D mouthpiece, submerged a trumpet in liquid nitrogen, and experimented with putting helium and Sulfur Hexafluoride through the trumpet. My resume is at the bottom.

Stereoscopy | Motion Capture | Trumpet Tube |