I want to implement the FDTD method to a discrete random media ( a medium which is filled with discrete scatteres randomly). the scatterers are also small (to the wavelength).
could you please introduce some refrences or papers that applied such method to the mentioned medium?
any tips, suggestion or experiences would be appreciated.
thanks in advance.
One technique is called the supercell method. Essentially you choose an area size that your computer can handle and distribute your particles around that. Then use periodic boundary conditions to make your particle collection seem infinite.
There are also closed-form models like Maxwell-Garnett and Bruggeman models. I have some information about these along with references in Lecture 12 here:
http://emlab.utep.edu/ee5390em21.htm
Dear Fateme,
The following paper describes electromagnetic simulation of randomly distributed particles in a dielectric matrix using CST EM Studio software:
K. A. O'Connor and R. D. Curry, "Three-dimensional electromagnetic modeling of composite dielectric materials," 2011 IEEE Pulsed Power Conference, Chicago, IL, 2011, pp. 274-279.
This paper also compares the computed results with a number of well-known closed-form mixture formulae. In the above paper, you'll see that Lichtenecker's logarithmic formula agrees very closely with the computed values. This formula was originally thought of as a semi-empirical one until I published a derivation of it in my paper of 2010 based on Maxwell's equations and the conservation of charge (citation below):
R. Simpkin, "Derivation of Lichtenecker's Logarithmic Mixture Formula From Maxwell's Equations," in IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 3, pp. 545-550, March 2010.
In that paper, the derivation of Lichtenecker's logarithmic mixture law is shown to be fundamental for a truly random mixture when the particles are small compared to the wavelength ( ie a quasi-static model). I also showed in this paper that the Maxwell-Garnett and Bruggemann formulae are approximations to Lichtenecker's logarithmic formula valid for weak coupling between particles.
In implementing a computational model for randomly dispersed particles, I would avoid introducing any kind of periodicity (eg a super-cell approach) since this could introduce spurious band-pass or band-stop behaviour that isn't representative of the actual behaviour of the material being modelled.
Hope this helps!
Thanks a lot Dr.Ray Simpkin for your great papers!
i am also interested in simulating random particles in CST at high frequencies (GHz ranges).
could you please introduce references or papers or etc that could describe more in detail how to create such medium (random particles) in CST?
thanks in advance! @ Ray Simpkin
Have a look at our Open Source FDTD simulator gprMax (www.gprmax.com) we use it to primarily model ground penetrating radar but is general enough to use in other areas. We regularly use inhomogeneous models for soils etc. that have stochastically distributed properties.
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