Stuck: finite difference method, grid coarseness

Hello.

I am trying to calculate the electrostatic field on a coupled microstrip enclosed withing a ground plane using finite difference method. the coupled microstrip rests on a 1mm thick dielectric, the rest is just air. The space where I compute the field is 5x5mm. 10V common mode is imposed on the coupled microstip.

I wrote some code in matlab and the problem is the coarseness of the mesh. That is for a mesh of 100x100 I get a very different solution compared with a mesh of 1000x1000 coarsness. I have been running simulations for ages now and I just can't tame the field. It looks ok on the picture, but there are several things that are wrong. For instance knowing how the field vector E behaves when going through the two dielectric (the tangens of the angle should be equal to the ratio of the relative dielectric constants).

Also looking at the field in the entire length of the space at 0.1mm above the microstrip (the two plots are included, red is the x component of the field, blue is the y component) one can see the two fields are very different.


Other info I can give you is that an Jacobi iterative scheme is used to solve the field and that at 100x100 grid there were 200.000 iterations (~2800 sec). The same number of iterations were done for the 1000x1000 grid (took a mere 45 hours).


I ofcourse tried with several grid densities (200, 300, 400 etc) and there always is some difference, I can't get the field to stabilise.

The code is always the same, boundary conditions are always the same. But the field isn't. I really do not know what to do next.


Please help

Any idea is welcome. Don't be shy.

can you send your code?