[Getdp] 3D conduction

[Benoit Bidoggia]

Hi,

I would like to solve a problem of electric 3D conduction:
in a non conductive region I have a conductive
region (or more than one, with different resistivities),
on some parts of the surface of the conductive
region I impose the total current (not the current
density, since I don't know its distribution yet).
The current may be dc current or ac-current,
so skinny effect, eddy current and so on should
be taken on account, I suppose.

Then, I would like to know what the distribution
of the current-density is.

Here my questions:
1) What kind of problem is this? Under which names
may I found it on books or on the net?
2) Is there a ready-to-use formulation for it?

E.g.: a cube of copper with two electrodes, one
on the cube and one under it, that don't cover
all the surface of the cube. The cube could have a hole
in its middle...

Best regards and
many thanks to every one could help me.

Benoit