What should be criteria to use for linear axes (x, y, z), boundaries, infinite, periodic, reflecting, or fixed

[rajxabc]

Hi Felix,
what should be the criteria to use axis boundary , in case of multiple pixel and single pixel for the same simulation.
in my case I've z axis fixed and remaining 'x' and 'y' axis i am not sure of . kindly look at the field lines.

[fhagemann]

The choice would depend on what describes your system best.
In the calculation of the electric potential, the potential value of each grid points is determined from its nearest neighbors.
At the boundaries of the world, there are no nearest neighbors beyond the volume of the world, so one needs to choose which value to choose there.

We have different options that are possibly best explained by another picture:

• periodic: for the right boundary, you would extend the world using the potential value of your left boundary. This would result in a simulated world that would periodically repeat in that dimension.
• reflecting: for the right boundary, you extend the world using the second-to-last potential value (ϕ(x_N+1) = ϕ(x_N-1)), which would result as if your world would be reflected at the last grid point of the world in that direction.
• fixed: you assume that the potential will just stay the same beyond the world (ϕ(x > x_N) = ϕ(x_N)). This makes sense if your world is defined by some sort of grounded cryostat wall.
• infinite: assuming that the potential decreases with ~ 1/x towards infinity, this boundary type will pretend that the potential approaches 0 using this ~1/x dependency. This makes sense if you have some object and expect the potential to relax to a

For your case, where you just want to simulate a single pixel in a multiple-pixel system (if I understand correctly), I would recommend either periodic or reflecting. This way, the simulated potential would resemble the potential that a system with infinite pixels in x and y would have. However, this potential then might not be correct for the outermost pixels, where the potential would not be periodically continued further out.

[rajxabc]

thank you Felix,
this is eloquent explanation (should be added to document file)

[fhagemann]

I'll be on vacation the next days, but I'll add this as issue: #479