Finite Differences in Inhomogeneous Media

Not Poisson's specifically but you can find a bevy of material on doing Maxwell's Equations. The seminal paper is the Yee algorithm but you can find discussions about FDTD in Chew's Waves and Fields in Inhomogeneous Media or Jin's The Finite Element Method in Electromagnetics (not the best books on the subject but I can't remember the third text I am thinking of, author's name starts with a "T"). Probably the main thing that you need to learn is defining the stability conditions and looking into absorbing boundary conditions or perfectly matched layers though the latter is negated by sufficiently increasing the problem space.

EDIT: Taflove! That's his name. He has a great textbook all about FDTD. If you want to take a look at how to solve Poisson's equation using another technique, Harrington's text discusses how to solve it using the Method of Moments but adding inhomogenous medium makes it a little more annoying.