## RCS calculation for multiple frequencies

How to use openEMS. Discussion on examples, tutorials etc

Moderator: thorsten

LowDepth
Posts: 20
Joined: Mon 10 Nov 2014, 16:59

### RCS calculation for multiple frequencies

Hi everybody,
I am trying to obtain the monostatic RCS of a perfectly conducting sphere as a function of frequency.
My sphere has a radius R of 25 mm and the frequency range I am interested in leads to products of
wavenumber times radius of kR > 10. Unfortunately the numerical errors at kR > 5 are already significant.

My questions are:
- Is there a primary source of the numerical errors in my (attached) setup? If I increase the mesh resolution from
lambda/20 -> lambda/30 results do look better, but I hope I am doing something wrong and the accuracy can be
increased without further refining the mesh.
- What does the numerical phase correction in the function 'AddPlaneWaveExcite' do and what kind of
value should I choose, if a have a wave with f_start = 0.1e9 Hz and f_stop = 20e9 Hz.
- Can I reduce the simulation volume by means of PEC and PMC boundary conditions if my scatterer has
symmetries? If yes, how should I choose the plane-wave box and the nf2ff box?
- Can "mirroring" be used in the NF2FF for more than one direction? So, does something like:
'Mirror', {2,'PMC',0, 4, 'PEC, 0}
make sense?

Best regards
Stefan
Attachments
sphere_rcs.m
Results for a mesh resolution of max_res = c0 / f_stop / unit / 30 with f_stop = 20 GHz
Mie_openEMS_30.png (26.22 KiB) Viewed 6766 times
Results for a mesh resolution of max_res = c0 / f_stop / unit / 20 with f_stop = 20 GHz
Mie_openEMS_20.png (26.55 KiB) Viewed 6766 times

thorsten
Posts: 1438
Joined: Mon 27 Jun 2011, 12:26

### Re: RCS calculation for multiple frequencies

Hi,

yes in theory you should be able to use PEC and PMC to quarter your simualtion domain, but be careful with the PMC, the symmetry center there is in the middle of the first (or last) mesh cell!

I hope you are using a homogenous mesh?
You can check if there is a problem with the plane wave phase correction if you simulate an empty space. The wave should disappear outside the plane wave domain as good as possible. But this is always difficult for large simulation domains...
Have you got any new findings in the last couple of days? (I have not yet checked your simulation script)

regards
Thorsten

LowDepth
Posts: 20
Joined: Mon 10 Nov 2014, 16:59

### Re: RCS calculation for multiple frequencies

Oh, I wasn't aware of this "half-cell" shift for the PMC condition, but it's of course plausible due to the shift of E/H (u/i) fields.
1. How should one deal with PMC-conditions? Say I have a PEC boundary at x = 0 and a PMC boundary at y = 0 and
mesh.x = [0, 1, 2, 3, ...]
mesh.y = [0, 1, 2, 3, ...]
Will this result in a PMC condition at y = 0.5?

2. Why is it bad, if I use a graded mesh for RCS simulations? For my PEC sphere I didn't, but once I get to dielectric bodies I would
have refined the mesh in the dielectric body...

Is your suspicion, that the increase of the amplitude of the RCS as a function of frequency is due to an incorrect phase center and
therefore everything gets better if the mesh is finer?
I will try a simulation with an empty PlaneWaveBox and post my findings.

Best regards
Stefan

thorsten
Posts: 1438
Joined: Mon 27 Jun 2011, 12:26

### Re: RCS calculation for multiple frequencies

Will this result in a PMC condition at y = 0.5?
Yes indeed. If you want it at y==0 then you need a "mesh.y = [-0.5, 0.5, 1.5, ...]"
2. Why is it bad, if I use a graded mesh for RCS simulations?
The numerical phase error has to be compensated as much as possible. While there is an approximation for a homogenous mesh, it is much more difficult for inhomogenous meshes.
For small TFSF areas this is all not a big issue, but for large domains (multiple wavelength) it starts to be an issue...
See here: https://github.com/thliebig/openEMS/blo ... .cpp#L2067

Your empty plane wave trial will show the problem...

regards
Thorsten

LowDepth
Posts: 20
Joined: Mon 10 Nov 2014, 16:59

### Re: RCS calculation for multiple frequencies

Hi Thorsten,
at an peak amplitude of 1 V/m for the electric field vector of my pulse, I get an amplitude
of 1e-3 outside the plane-wave-box. Is this okay, or too high?

thorsten
Posts: 1438
Joined: Mon 27 Jun 2011, 12:26

### Re: RCS calculation for multiple frequencies

Hmm, I don't know, sounds still a bit high...

what kind of resolution do you use? I think to hold the numeric dispersion and phase error in check you really need something like 30 to 40 lines per wavelength (at your max. target frequency)...