A simple problem on solving Poisson's equation

Dear all,

I'm solving a Poisson's equation for a charged cylindrical shell structure.

The model has cylinrical and z-invariant symmetries, i.e., only inhomogeniety in r direction exists. On the shell (of certain thickness) there's a fixed distribution of electric charge, and the net charge is zero. Inside and outside the shell is just vacuum.

I want to solve for the electric potential in 2D. For such a charge distribution the potential should be constant both inside and outside, and continuously connected across the shell.

In the model a reference value of the potential must be specified somehow. However, this Dirichlet constraint gives physically different results (not only the shift of reference) when imposed at different positions in the configuration. Particularly, the potential inside/outside doesn't approach a constant value away from the shell if the constraint is imposed inside/outside the shell. If I put the constraint at a position within the shell body, the result is reasonable, the potential goes to constant in both two directions away from the shell.

Does anyone know why the constraint induces physically different results? What should I do if I need to specify a reference potential inside or outside the shell?

Thanks a lot for reading my lengthy problem, anyway!