Perfectly Matched Layer for a Standard Wave Equation

How do you add decent absorbing boundary conditions so that you can pretend you're simulating real electromagnetic phenomenon except inside of a computer? How do you do this when you're not solving Maxwell's equations, but wave equations for potentials and not fields? Well look no further: this does just that by using a, "standard," analytic continuation of spatial coordinates into the complex domain, and then discretized and solved using a few different techniques:

1. A fully explicit finite difference method using first order equations via an auxiliary differential equation,
2. A fully explicit finite difference method using second order equations,
3. A semi-implicit finite difference method using first order equations via an auxiliary differential equation.

The nice thing about these methods is that the exact same files should work exactly the same in 3D (albeit quite slow and memory intensive) because MATLAB is rad like that. The included PDF discusses some of the theory behind this work, with a very good reference to start with being:

http://math.mit.edu/~stevenj/18.369/pml.pdf

With the exception of setupPML.m each of these files is a standalone file that you should be able to run to see how things play out for a standard oscillating source charge distribution.