I am solving EM wave scattering by PEC cylinder numerically and wanted to compare the scattering width. My result is in the time domain which is evolving with time but the analytical solution is not a function of time. So I have two questions regarding this -
1. How do I compare my time domain result. At what time should I compare my result, since the wave is propagating in all direction with time in my numerical simulation? (figure - 1)(figure -2 1D plot)
2. Analytical solution has complex value result, which absolute value is used to compare the scattering width result but my result is in real value so how do I compare the result. (figure 3)
[In figure 3 I have shown comparison with analytical solution real part, how do I compare with absolute part since I only have real data from numerical solution]
Any help will be appreciated
Hi Jamal,
If you multiply your analytical solution by the harmonic time factor exp(jwt), where w is the angular frequency and t time, and then take the real part at any time of your choosing, you should get a direct comparison with your real-valued time-domain solution. This assumes you've used a harmonic excitation (ie a sinusoid) for your time-domain numerical model and have allowed sufficent time to elapse for the field to settle down to its steady state.
Hope this does the trick :)
Regards,
Ray Simpkin
To get analytical representation in the time domain you should start with Fourier transform of the signal, then scattering depending on wavelength, and then inverse Fourier.
Frequency domain simulation give you the 'permanent' response of the system at time = + infinity, for one frequency. You never access this regime in time domain.
If you simulate a time response of 'T' seconds in time domain, you need to compute and coherently sum in frequency domain over a 1/T (Hz) frequency bandwidth to get similar results.
The Heisenberg relationship gives you the exact correspondence between temporal and frequency resolution... Be careful with reverberation.. If your analytical solution is for infinite media and the time domain simulation use reflecting boundary, you need to select the early time of the simulation propagation (before the wave come back) and sum over a larger frequency band (corresponding to the frequency resolution of your time-domain simulation) your analytical formulation for comparisons.
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