I would like to calculate the potential due to a point charge in the proximities of a conducting cylinder. For this I started by calculating the potential due to the point charge alone using the Poisson solver implementation inside Intel MKL ( s_Helmholtz_3D subroutine, based on one of the examples of the MKL, see attached file).
Now the problem is how to impose the boundary conditions (Dirichlet) due to the presence of the cylinder (V=0 in its surface if it is grounded). The system looks like the attached figure. Is there a way to impose the inner boundary conditions using the MKL Fast Poisson solver implementation?. If that is not possible, what approach would you recommend to tackle this problem?
I have tried this problem with an iterative multi-grid solver, but it is painfully slow, therefore I am searching more efficient ways to solve this problem. I really appreciate your help!.