On Aug 19, 2009, at 11:09 AM, Roy Zhang wrote:
I'm using MEEP to deal with a problem which require a model with
exact epsilon value in each pixel.
However, as you know, MEEP will modified the model automatically to
average the epsilon value at the surface of different kinds of
dielects. Such situation is not allowed in my simulation. I just
wondered how can I turn off the anisotropic averaging function,
because it seems that although I've already tried 'eps-averaging' in
ctl mode and 'set_epsilon' in C++ mode, the averaging is still can
be found in output files. Can I turn off this function just by
setting some parameters in MEEP or do I have to modified the source
code of MEEP? This really troubles me a lot.
This has been covered on the mailing list before:
http://article.gmane.org/gmane.comp.science.electromagnetism.meep.general/1720
When you set eps-averaging? to false, Meep performs no smoothing and
simply samples your dielectric function at each pixel (resulting in
"staircased" structures). However, when it outputs to an HDF5 file it
has to interpolate from the staggered Yee grid onto the center of each
pixel. This is not an "averaging" within the simulation itself, but
is a form of averaging in the HDF5 output only.
However, stepping back from your question for a moment, I want to be
sure that you know what you are doing.
Realize that FDTD algorithms (like Meep) are not solving Maxwell's
equations, they are solving a discretized approximation to Maxwell's
equations. So, it is usually nonsense to ask for the "exact"
discontinuous epsilon function, because whatever you put in is not
exact by virtue of the fact that it has been sampled into difference
equations on a grid. The real question is (usually) how one can make
the discretized solution converge as quickly as possible to the
solution of the exact Maxwell's equations as you increase the
resolution. A major motivation of the subpixel smoothing is that it
generally makes the solutions converge *faster* to the solutions of
the exact Maxwell's equation with discontinuous materials than doing
no smoothing at all. (See our papers.)
Regards,
Steven G. Johnson
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