convergence issue

[alireza shabani]

Dear FDTD users,
I have a problem with convergence and stability of the results in the FDTD calculations. I employed the Optiwave package to simulate Titanium nitride split ring resonators (also complementary SRRs). The problem is that there are some fluctuations in the optical transmission spectrum that may be due to lack of convergence in simulations. Which parameters involve in the convergence process? Is it enough to change the Mesh parameters or time steps and time step size? Is there any additional parameter to be considered?
any help would be thankful.
Best regards,
Alireza

[Scott Newman]

Hi Alireza,

Typically a convergence test is looking at the convergence of a value relative to the Mesh size. However, you must keep in mind that when you change the grid size you must also change the time step size in order to ensure stability. The condition for this is the Courant-Friedrichs-Levy condition and is dt <= (v*sqrt(dx^-2+dy^-2+dz^-2))^-1 for 3D and dt <= (v*sqrt(dx^-2+dz^-2))^-1 for 2D.

You can either manually calculate this or simply leave the dt and number of time steps checked to auto and the software will perform the calculation for you.

Scott

[alireza shabani]

Dear Scott,
thanks you for your comprehensive response.
how can I activate the automatic check in the software? I have attached 3D simulation window that shows the time step size and I circled the auto box.
what about the time step, is it effective in the convergence process?
thank again for your helpful comments.

all the best,
Alireza

Attachments:

1. 

   sssss.png
   

[Scott Newman]

Alireza,

You will also want to check the auto box for the number of time steps because if you do not then each simulation in your set will have a different simulation time. Think of it this way based on a dt of 6.67128190396304e-18 and 4000 time steps your simulation will be over a time of 26.685 ps. However, based on your settings if you half your grid spacing your dt will become 3.3356e-18 s so if your 4000 is fixed and not on auto this second simulation will be over a time span of 13.343 ps.

Scott

[alireza shabani]

Dear Scott,
thank you for your help

Alireza

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