Thanks for your explanation. Just to clarify, could you elaborate as to
why the convergence is first order with dispersion, but second order
otherwise?
In a test case where I have an analytic result (lossy slabs), I've found
the covergence leaves room for wanting. Is there anything besides the
resolution which might cause a very slight shift in frequency? The
analytic result is a frequency domain method, using the same lorentz
model for the perimittivities as the one I input into meep.
Best Regards,
Matt
On Fri, 29 May 2009, Steven G. Johnson wrote:
On May 29, 2009, at 11:55 AM, matt wrote:
I was wondering how well eps-averaging works when the materials are defined
as lossy.
I guess that meep is basing it's averaging on eps_inf and not on the full
complex permittivities. Is that correct? If so, what does it mean to have
eps-averaging enabled with lossy materials present?
Correct, Meep currently only does subpixel averaging of the nondispersive
part of epsilon (and mu).
The dispersive part is not averaged at all. This means that any sharp
interfaces between dispersive materials will dominate the error, and you will
probably get only first-order convergence, the same as if you do no no
subpixel averaging at all.
It's possible that the subpixel averaging may still improve the constant
factor in the convergence if not the asymptotic convergence rate, if you also
have a lot of interfaces between nondispersive materials or if the dispersion
is small (i.e. if epsilon is close to \epsilon_\infty over your bandwidth).
On the other hand, if the dispersion is large and most of your interfaces are
between large-dispersion materials, then subpixel averaging may not help at
all and you might as well turn it off.
The subpixel averaging shouldn't hurt you, though, except possibly in
performance.
Steven
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