A numerical solution of cylindrical coordinate Laplace’s equation with mixed boundary conditions along the axis of symmetry: Application to intracerebral stimulating electrodes

Abstract

A numerical solution method of Laplace’s equation with cylindrical symmetry and mixed boundary conditions along the Z coordinate is presented. The method is based on an iterative process. It is applied to the evaluation of current density distribution in the region surrounding electrodes used for intracerebral electrical stimulations. The procedure converges quickly and after only twelve iterations the boundary conditions are satisfied within an accuracy of 0.1%. The convergence criterion is discussed and the results obtained on the current density distribution are presented.