Posted on July 4, 2015
A variety of commercial software tools exist for finite element method (FEM) and finite difference time domain (FDTD) simulations, and I prefer to use those, but sometimes an unusual problem calls for more control or customization of the simulation than a commercial package can give.
I have experience writing FEM and FDTD simulations from scratch in Matlab and am familiar with a variety of techniques including successive over-relaxation, Crank-Nicholson, staggered leapfrog, to solve a variety of physical problems related to gas dynamics, linear and nonlinear wave mechanics, thermal diffusion, and so forth.
The simple examples below are 2D simulations because they are easier to visualize (3D simulations require cross-sections to see inside them, so you end up looking at a 2D image anyway), but 3D simulations are really not much more difficult.
Poisson equation showing electric field leaking into a grounded electrostatic “cage”
A Gaussian pulse excites a wave on a simple rubber sheet. Any driving function may be used and a variety of linear and nonlinear wave equations may be substituted, but the results are not quite as beautiful!
[More coming soon…]