Hello everyone, I am doing a 2D time domain simulation now. The system contains two layers, the top is air and the bottom is a mateiral whose permittivity changes in time and is step-function like (I defined a piecewise function called 'pwl_epsr' in the global defination). You can leave alone the background of this problem, because it is just a simplified model. Please see the attached Fig1 and Fig2 for the schematics of the system and the permittivity profile of the bottom material.
The electromagnetic wave is incident from above (in -y direction), and I used scattering wave boundary condtion as exitation source, because 'port' boundary is unavailable in time domain. In x direction, I used perfect electric conductor. I have also benchmarked my system by illuminating a single air box with scattering BC. The field pattern looks good and it is indeed a beam of plane wave propagating.
But, when I tried to add the bottom layer, things went wrong. I animated the electric field along y axis versus time. At first, it still looks good, after some time, however, the electric field explodes to infinity. It is an obviously unphysical result and I am not sure what happens.
I guess there is no problem with my source because I have benchmarked it. The only thing that can go wrong is the material. I suspected that the abrupt change of material property is intrinsicly unphysical, so I smoothed it using the built-in smoothing function. I also adjusted the time step to increase accuracy according to the guidance here. But none of the methods worked. Can anyone help me with that? *I have attached my simulation file, you just need to run it and see some plots and animations I've made. *Thank you very much!