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We calculate electrostatic potential landscapes for an external probe chargein the presence of a set of metallic islands. Our numerical calculation inthree dimensions (3D)uses an efficient grid relaxation technique. Thewell-known relaxation algorithm for solving the Poisson equation in twodimensions is generalized to 3D. In addition,all charges on the system, free aswell as induced charges,are determined accurately and self-consistently tosatisfy the desired boundary conditions. This allows the straightforwardcalculation of the potential on the outer boundary using the free spaceelectrostatic Green's function,as well as the calculation of the entirecapacitance matrix of the system. Physically interesting examples of nanoscalesystems are presented and analyzed.Comment: 6 pages, 6 figures, submitted to PR

Potential landscapes and induced charges near metallic islands in three dimensions