Hello, I found a way to make my simulation stable for any (?) given simulation time. The Z-size of the simulation volume must be extended so that the PMLs are far from the simulated resonator. (It does not depend on the PML thickness if it is reasonable.)
Separation of approximately one vacuum wavelength prevents the oscillation onset for more than 1000 periods, which is what I needed. It seems that the resonator couples by near-field to the absorbing layer and that there is some frequency for which this combination tends to invert the losses into gain. Briefly, one can say that "resonator + PML = oscillation". Filip >> On Thu, Apr 12, 2012 at 12:00 PM, Filip Dominec >> <filip.domi...@gmail.com>wrote: >> >>> Dear Meep users, >>> today I am writing because I observed an unexpected behaviour of my >>> simple simulation: >>> A dielectric resonator of spherical shape is defined in center of the >>> volume, through which a broadband gaussian pulse is sent in the Z >>> direction. The X, Y faces of the volume are defined to be periodic, >>> the Z faces are equipped with PML (thickness = lambda/10). The >>> transmitted and reflected waves at the Z faces are recorded and >>> finally processed by custom FFT. >>> >>> Although for first part of the simulation everything works as >>> expected, the electric field starts to oscillate in a exponentially >>> growing _transverse_ mode after a longer run. This limits the spectral >>> resolution of FFT and ove From MEEP mailing list, I learned that FDTD >>> simulation may become unstablerall simulation accuracy. >>> >>> I prepared a specialized page with illustrative images: >>> http://fzu.cz/~dominecf/misc/meep/instab_long_run/ >>> >>> The oscillations seem to depend on the number of simulation steps, so >>> with coarser grid and greater time step the simulation starts to >>> oscillate at a later time. >>> Changing Courant factor from 0.5 to 0.01 resulted in much longer >>> simulation only, but oscillations surprisingly occured at the same >>> time. So it is perhaps a numerical, not electrodynamical problem. >>> >>> From MEEP mailing list, I learned that FDTD simulation may become >>> unstable >>> 1) for non-dispersive real negative epsilon [1], or >>> 2) for any non-dispersive complex epsilon, where (f * Re(eps) < 0) [2], >>> or >>> 3) for dispersive epsilon with resonance frequency too high [3]. >>> However, I am using real epsilon=94. >>> >>> I would be very thankful if somebody pointed me out where such >>> oscillations may come from! >>> Filip Dominec >>> ____ >>> [1] >>> http://www.mail-archive.com/meep-discuss@ab-initio.mit.edu/msg02450.html >>> [2] >>> http://www.mail-archive.com/meep-discuss@ab-initio.mit.edu/msg02455.html >>> [3] >>> http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Numerical_stability >>> >>> _______________________________________________ >>> meep-discuss mailing list >>> meep-discuss@ab-initio.mit.edu >>> http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss >>> >> >> >> >> -- >> Abdullah Al Rashid >> >> Graduate Student >> Theory of Nanophotonics and Photonic Materials >> Department of Physics >> University of Toronto >> >> Mailing Address: >> 60 St. George St >> Toronto, ON M5S 1A7 >> Canada >> >> Telephone: +1-416-978-5207 >> E-mail: abdullah.alras...@utoronto.ca >> > _______________________________________________ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
