Finite Differences in Inhomogeneous Media

[Excom]

Hi

I am trying to solve the Poisson equation, with the use of the Finite Difference Method, for a inhomogeneous media with some charge distributions embedded in the media.

Is there anyone that know some literature, which treats this subject?

Thanks in advance

 

[Born2bwire]

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.

 

[charng]

for any help.

I am familiar with the use of the Finite Difference Method for solving the Poisson equation in various media. Inhomogeneous media, where charge distributions are embedded, can be challenging to solve using this method. However, there are several literature resources available that discuss this topic. Some examples include "Finite Difference Methods for Partial Differential Equations in Inhomogeneous Media" by John Strain and "Finite Difference Methods for Electromagnetics in Inhomogeneous Media" by Weng Cho Chew. Additionally, there are also many research papers published on this subject that may be helpful. I recommend consulting these resources to gain a better understanding of how to apply the Finite Difference Method in inhomogeneous media.