interface para mu

Any one can give me some guide to deal with the interface parameters using FDTD
especially for permeability .

I think this is a topic which is not treated adequately in textbooks or papers. One (not very helpful) way of thinking is: choose whatever you like, if you start reducing the grid size then everything converges to the same result.

More seriously; first it is a good idea to handle conductivity on the one hand and permittivity and permeability on the other hand separately.

I have run across the following averaging methods.

METHOD A
1) for each Yee cell generate parameters (any kind of averaging, staircasing).
2) average the Yee cells touching a field location.
(i.e. for H-fields average 2 and for E-fields 4 Yee cells)

METHOD B
1) draw a cube of a user settable size around each field location (EX, ... HZ)
2) average the permittivity/permeability in this cube

METHOD C
1) Draw an arrow in the field direction going through the field location. (for EX and Yee cell 0,0,0 the arrow goes from 0,0,0 => 1,0,0 since the ex field is at 1/2,0,0)
2) average the permittivity/permeability along this arrow (I have never seen anybody mention the case where different materials touch but not intersect this arrow, but I guess then you average the angles)
Method C consists basically of slightly enlarging the arrow and then taking volume averages

There are more complicated methods where you take the interface orientation into account (search for subpixel smoothing with {scr,g}oogle) but I have not used them seriously yet.

Also if one material is a PEC or PEC covered by a thin layer of some material you have again a whole lot of methods to chose from (e.g SIBC or some locally conformal methods)

No matter which method you choose you should check how they behave when you shrink the grid size. Depending on your models there may be a "best" method. I also would start with the simplest method check how it behaves under grid size variation before proceeding to the next method.

Thanks.
I am still confused how to deal with the interface if there are some dispersive materials such as debye ? Still average?

And when one material is a PEC covered by a thin dispersive layer of some dispersive material, do i need to use the average method ? The locally conformal methods looks they don't use averaging.

If i do nothing about the interface, will the results converge and be accurate?

Very thanks

There does not seem too be much material available. There was one paper which essentially said
averaging at interfaces between dispersive materials is a good idea. (I requested this paper a
while back and somebody posted it about a month ago but I cannot find it right now.)
However it depends on how you implement your dispersive materials. Roughly you average the
modified eps/sig/mu or the polarization currents. But I think this would have to be checked for
each method individually.

But for PEC covered by a thin dispersive layer I think the only method I remember seeing was in

Subcell FDTD modeling of electrically thin dispersive layers, Karkkainen, M.K.
Microwave Theory and Techniques, IEEE Transactions on

No they don't average because they try to approximate the local situation more accurately.

Depends on the model. I recently read in one paper that for curved boundaries the standard
methods (including averaging) do not converge. I did not check any details and cannot recall
the paper now. I might be able to find it again though.

" Subcell FDTD modeling of electrically thin dispersive layers, Karkkainen, M.K.
Microwave Theory and Techniques, IEEE Transactions on "

I know this paper and want to use it to develope my FDTD code. That is why i am confused here. This paper didn't mention anything about the interface. If the cells under the thin dispersive layers are different , for example, air or the same dispersive materials, if we don't use average method, can we get accurate results?

Could you dig out the other paper you mentioned ?

Thanks

I don't have this paper so I cannot really comment on details.


Somebody else posted it for me but it seems to have vanished. Here it is.
("Effective permittivity at the interface of dispersive dielectrics in FDTD, Popovich&Okoniewski)