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.
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.
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