Effective 3-dimensional electric field calculation by surface charge simulation method

Details concerning fast and accurate electrostatic field calculation techniques based on the 3-dimensional surface charge simulation method by means of Fourier-type charges are presented. The techniques range over (a) the direct potential and field coefficient formulas, (b) a computation of Legendre function of the second kind with half integer degree¿¿toroidal function Qm¿¿¿¿(x), (c) a high-speed integral and (d) an introduction of the associated toroidal function Sm¿¿¿¿(x). As an example for application, a tilted hemispherically tipped cylindrical rod electrode with a spherical dielectric is analysed and the results are demonstrated.