I am looking for solutions to Laplace equation for two eccentric cylinders in 3D with arbitrary boundary conditions. The boundary condtions also depend on the axial variable.
I tried to work with Bessel-function solutions in cylindrical coordiantes for each of the cylinder separately and merge them at the boundary by expanding the solutions for one of the cylinder in terms of the Bessel functions in the other coordinate system (centered on the interior cylinder). Unfortunately, when evaluting numerically this produces numerical problems due to singularity for r=0.
I read about the bipolar cylindrical coordinates, but I could not find the solution for my specific three-dimensional problem. My ultimate goal would be to generalise the solution for more than one inner circle.
How can I approach the problem?
