Automatic arrangement of fictitious charges and contour points in charge simulation method for two spherical electrodes

We propose a method to decide the appropriate arrangement of both fictitious charges and contour points in the charge simulation method for the case that the shape of electrodes can be expressed in the spherical coordinates. In this paper, we use genetic algorithm (GA), which is inspired by the mechanism of natural selection where stronger individuals are likely the winners in a competing environment, as a search method. We calculated the potential distribution around two spherical electrodes with different potentials above a grounded electrode plate. The surface potentials of the electrodes were assumed to be 5000 and 30 V, respectively, for example. The total number of the charges was 22 for the electrode system. First, we placed fictitious point-charges and contour points at random inside the electrodes and on the surfaces of electrodes, respectively. The arrangement was automatically adjusted by using GA until the potential reached the desired values at all the test points placed on the electrode surfaces. We show that the GA can be useful to determine the appropriate arrangement of both fictitious charges and contour points simultaneously.