Alright, I uploaded the examples and some notes (notes.pdf) on github, I hope this helps. The repository also contains my changed versions of the meep.hpp and sources.cpp that are needed for plane wave illumination. Any changes I made there are marked with "fesc3555".
https://github.com/fesc3555/meep_variable_resolution.git > That's great to hear; I've suggested using transformation optics for variable > resolution several times on the mailing list, but I can't recall whether > anyone actually succeeded in doing it. (The formulas are all well known, but > implementing them can be tricky.) You're right. So far I wrote explicit formulas for the transformation of purely isotropic epsilon, this at least is straightforward. The backtransformation I did in octave. Getting the correct fields back near the domain boundaries is not easy, I think because of anisotropic averaging and the yee-shift. However, i can live with a couple of lines where the fields are hard to correctly transform back, because I measure nothing interesting along these lines anyway. >> 2. I do scattering calculations, using dft_flux_box-es. I am a bit >> confused: do I have to watch out for something, if I put these boxes in >> the region with the transformed epsilon an mu? Transforming the fields >> back somehow before the flux is calculated? > That's a good question. Of course, transforming the fields back before the > flux is calculated will definitely work in principle, but it would be a pain > to implement. > > It's possible that you could just compute the "ordinary" flux in the > transformed region and it will just work (i.e. give the same answer as the > flux in the original coordinates), but I'm not sure about this. I can think > of a couple of cases off the top of my head where it must be true, but I > don't know if it is true in general. > > It should be a straightforward exercise to check this. Look at my notes on > transformation optics > http://math.mit.edu/~stevenj/18.369/coordinate-transform.pdf > and plug the transformed fields into an integral of the Poynting vector > (don't forget the Jacobian factor for the integral itself), and see if you > can show that it is invariant under the transformation. (Note the tricks > with the Levi-Civita tensor and identity after equation (17), for example.) Should be done, please see the respective section in the notes.pdf under the git repository given above. I hope this is correct, it's been a while... In my example simulations, it works perfectly fine so far. The dips/wriggles mentioned earlier were indeed only artefacts of the small resolution in combination with a metal. Regards, Felix -- Felix Schwarz Technische Universität Ilmenau FG Theoretische Physik I Tel: +49 3677 69 3644
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