I recently read Kane.S.Yee's paper on FDTD (link provided). To my understanding, the paper provides an algorithm to simulate EM wave propagation by discretizing space and time to sufficiently small scales.
What confuses me is the proposed equations (14a)-(14c), regarding the iterative method to calculate electric and magnetic fields. To be specific, the author assumed that he was simulating a plane-wave propagating toward a perfectly conducting square along the X-axis (while E-field having only Z-axis component and H-field having only Y-axis component).
I expected to see the permittivity & permeability profiles of the "perfectly conducting square" and the rest "finite space" in this case, but neither of them is mentioned--instead, the author used a constant Z=sqrt(µ/ɛ)=367.7 in his equations to do the simulation. I'm curious about how boundary conditions of the obstacle were dealt with by his equations without mentioning the permittivity & permeability profiles. For this problem, I think Z=Z(x, y)=sqrt[µ(x,y)/ɛ(x,y)] would be necessary to do the simulation.
http://ecee.colorado.edu/~mcleod/pdfs/NMIP/references/Numerical%20Solution%20of%20Initial%20Value%20Problems%20of%20Maxwells%20Equations%20Yee%201966.pdf
Figure 2 shows how to handle the PEC square : by enforcong Ez=0 on the square's surface.
Note that Yee's paper is the foundation of FDTD method for electromagnetism, but there has been a huge number of papers and books dealing with this method afterwards, where you can find many more useful information on meshing, computation, boundary conditions, stability conditions, etc.
Just try to Google "book fdtd"...
To add to Fabrice's answer, I can highly recommend Taflove's FDTD book: http://www.amazon.com/Computational-Electrodynamics-Finite-Difference-Time-Domain-Edition/dp/1580538320.
Hi, in this paper the equation is not solved in the area of the conducting square, just outside. Since at the boundary, the values of E and H are forced constant, any pulse is reflected and solving inside would make no sense. Hence the material constants of the conducting area is not needed for the simulation.
Thank you all for the replies! Actually I am writing a program to simulate the sample mentioned in Yee's paper, and I want to avoid using [if … else …] statements to deal with boundaries during the iteration. I have tried applying a rough profile to this problem and it yielded a satisfying result :) I'm going to proceed to the rest part of the paper.
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