SIMION 3D is a widely used ion-optics simulation program in many branches of physics. In SIMION, electrostatic fields can be modelled as boundary value problem solutions of an elliptical partial differential equation called the Laplace equation. The specific method used within SIMION to solve this equation is a finite difference method called over-relaxation. This technique is applied to a three-dimensional potential array (PA) of points representing electrode and non-electrode regions. The objective is to obtain a best estimate of the voltages for the points between the electrodes. The three-dimensional array is chosen to have either cylindrical or planar symmetry or no symmetry at all. The Laplace equation has the convenient property that its solution is a sum over the contribution from each electrode. Therefore, after the electric field array has been found once by iteration, the voltages of the individual electrodes can be changed and the new fields are immediately obtained.