To find the reflection factor using fourier transformation of the reflected pulse, we are given dx, dt, and other usual constants like speed of light, epsilon, mu0 , theta, omega, frequency. we are also given R(0), number of cells.
My question is: in the formula which u have mentioned: FT(R, w)/FT(P, w),
what is the value of R? is it R(0)?? How do u get P? Can u pl. elaborate on the formula which u have mentioned?
If you want to measure the reflection you have to do the following
1) run a FDTD simulation where you can measure the incoming pulse P and the reflected pulse R.
(often you use short pulses or pulses generated some distance from the reflecting region.
2) Both P and R are time signals. To get the frequency content at various frequencies you compute
either FFT or DFT of both P and R. (Above I used FT(R,w) to denote the value of the Fourier transform of R at the frequency w.)
.
Then the reflection factor is simply the quotient as I wrote above.
So far the easy part.
The more difficult part is how to get P and R. I am not sure what Berenger did since I don't have
access to the reference he cites. I assume the term Huyghens surface may be a TF/SF like method to introduce a planewave.
He used a Gaussian pulse. He measured the incoming pulse at a fixed location during the initial
part of the simulation. Then he made sure that the model was big enough that unwanted reflection
had no chance to reach the measurement point when he measured the reflection at the same point
(timesteps 100-200).
These measurements were the time signals P and R I mentioned above. The total measured signal
should roughly have the following shape
_/\____/\_____*******
the first peak is P the next R and eventually you will have lots of noise.