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# courant factor in 3D-FDTD

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#### ravi8331

##### Full Member level 4
courant factor

hello
how can i calculate the courant factor in 3D FDTD method.
anyone plz tell me how can i calculate the space cell sizes for a 3D geometry in FDTD????????

fdtd courant

Have you looked at any FDTD-book yet? Sullivan, Taflove etc. all have an explanation.
If you look for an exact treatment it will be a bit harder because the the above books
ignore the boundary conditions. (Which is not a problem since including the boundary
condition slight raises the limit for the maximal stable time step)

courant condition fdtd

i have gone through many books like Sadiku, Sullivan etc. but in all books they don't provide any formula or relation by using that i can calculate it................
uptill now i don't understand how can i determine the space cell size and courant factor in 3D geometry................

explanation fdtd

i have gone through many books like Sadiku, Sullivan etc. but in all books they don't provide any formula or relation by using that i can calculate it................
Sullivan p.4 for cubic grids:

dt <= dx/(sqrt/c)

dx = cell size
dt time step
c = 3e8m/s
n = 1,2,3 for 1d,2d,3d FDTD

detailed explanation is in Taflove

courant limit fdtd

hi

for the space cell size , it depends from the structure geometrie . Also, have you a dispersive environnement, homogene environnement etc.. to precise your cells parameters.

A+

fdtd stability factor

formula given by you is the CFL stability condtion for FDTD.
this is the courant factor???????????
i think courant factor is a factor by which the duration of a time step is determined with respect to the CFL stability limit.
so how can i calculate the this factor using CFL condition??????????????

material courant limit

rule of thumb for cell size is:
dx <= λ/20
where λ is the shortest wavelength you want to simulate, then, as already posted by iyami
dt <= dx/(sqrt(3)/c)
the Courant factor would be 1/(sqrt(3) which is the limit for stability.
I usually use .99*1/sqrt(3) but u might need a lower factor depending on what you are simulating (bear in mind that numerical dispersion is minimized at the courant limit).

courant limit

formula given by you is the CFL stability condtion for FDTD.
this is the courant factor???????????

You do like question marks don't you? (Here are some more: ????)

In any case I misunderstood your question since I could not believe anybody asking for the
Courant factor.

Basically you have 3 conditions to satisfy:

1) the Courant limit: dt <= CFL(dx,dy,dz,epsilon,mu) to make sure your simulation is stable

2) some similar condition for high conductivity materials (which is usually ignored by most people
and also depends on the discretization method)

3) a time step which is small enough to allow fine enough resolution of the shortest wavelength
of interest.

If your geometry is small compared to the wavelength you can ignore 3 and therefore anything
satisfying 1 is ok.

If your wavelengths are small then it depends on
a) the algorithm
b) the desired accuracy

For b) look at Taflove and 'numerical dispersion'

For a) standard FDTD => usually lambda/10-20 depending on your model.
(If you have very long models and phase matters, even lambda/20 may not be good enough)
For low dispersion FDTDs (NSFDTD/Forgy's FDTD etc) lambda/3-4 may be good enough

Summary:
numerical dispersion.

### ravi8331

Points: 2
fdtd courant frequency

Thanks dear for such nice and clear explaination..................
i am highly thankful to you........
here i want to simulate the probe feed rectangular dielectric resonator antenna (RDRA) of size 20mm length, 12mm width and 13mm height. for this RDRA i want to calculate space cell size and courant factor and also i want to calculate the return loss , input impdance and far field of this antenna.
i make code for this antenna using microstrip line feed but i am unable to make code for cylindrical object for coaxial feed...if you provide something related to cylindrical object then it will help me lot..............

fdtd modeling wavelength rule

here i want to simulate the probe feed rectangular dielectric resonator antenna (RDRA) of size 20mm length, 12mm width and 13mm height. for this RDRA i want to calculate space cell size and courant factor

here the materials and the highest frequency you need to consider matter to figure out a reasonable dt

and also i want to calculate the return loss , input impdance and far field of this antenna.

here far field computation is probably the most painful to implement

i make code for this antenna using microstrip line feed but i am unable to make code for cylindrical object for coaxial feed...if you provide something related to cylindrical object then it will help me lot..............

for cylindrical objects a first reasonable approximation is to compute average of the materials
(epsilon,sigma,mu) for each cell (whatever cell size you use). This gives in my experience quite
reasonable results (10 cells diameter may be good enough).

In any case some experimenting with different cell sizes is much easier than using some
rules to decide the cell sizes before hand. So I would make sure that my code allows for
variable cell sizes.

thanks ....
can you please send me your code for cylindrical objects.i am highly thankful to you.
plz send me at my mail id ravi8331@gmail.com
thanks once again.....

as much as I would like to I cannot (unless you have lots of money).
But you don't need any heavy machinery. All you need to figure out is the area
of each grid cell covered by the cross section of your cylinder. (Wikipedia should
have all needed formulas). Then use that area as a weight to average the parameters
for the materials in- and outside the circle. Then run your program (No rocket science
needed)

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