Solving BVP PDE in 3D

Is there a current, ready to use, Matlab tool/function that can be used to solve a BVP PDE that has 3 different, spatial components within it (aka 3D) or is the PDE toolbox using FEM the only method available before having to apply a fully customized FDM approach? Basically I wish to solve the Poisson equation in cylindrical coordinates given a specified current density J:

Expanded:

Where is a piecewise function representing the different material types. The equation has already been reduced to a single, spatial dimension component for my application which I attempt to indicate via the s.

The only other option I could forsee was after finding the Electormagnetics tool and possibly specifiying "Electromagnetic Model" for the "createpde" but it reduces the model to 2D by assuming symmetry around the axis of rotation and A has no symmetry in any dimension, so this cannot be used.

So to recap, these are the potential options:

1. Matlab PDE Toolbox with FEM
2. Custom FDM approach

Would like to confirm if these are all my options or if there are others.

Answer 1

[Torsten]

Would like to confirm if these are all my options or if there are others.

Using MATLAB, these seem to be the only options. And you should confirm in advance whether the PDE toolbox can cope with cylindrical coordinates.

[John]

Thank you for the response Torsten. Exterior to the Matlab context, do you recommend anything else that would be relatively easy to pick up/use? I was recommended Comsol by a peer as an alternative for simulation work and am open to more suggestions.

[Torsten]

Yes, COMSOL - especially for the solution of general PDEs - would be my choice, too.