FDTD problems [big sigma causes negative coefficient]

I was doing some simualtion with the time variant sigma and current using FDTD. The problem is that the sigma is larger than 1 { my time step is 1 ns,can not be smaller than this value } which will cause the coefficient of the iteration for E fields

factor = epsi-sigma*dt/2 negative, then cause osillation of my simulation.
Are there some gurus can give me some advice on how to deal with this issue.

Thanks

That is a situation conveniently ignored in most textbooks.
In fact I think this is another CFL-like codition.

In general your options are

1) smaller time steps
2) replace the conducting material by PEC
3) use an exponential discretization of Maxwells equation

1) is usually not a reasonable choice (nobody wants to use too small time steps)
2) is a reasonable choice in most cases
3) may be the best option but you need to find one of the few papers which describe/derive the formula

Thanks
I would like to try the third one. Where can i find the papers ?

search for "exponential discretization" using your favorite search engine?

Most of these papers are 'for members only'. If you are at a university which is a member of the
relevant organization you can download them.

I cannot.

Have a look at the last lectures at

http://www.ece.udel.edu/~dprather/cl...840/lectnotes/

There is some explanation of "Exponential Time Stepping" which is the
same thing as exponential discretization.