Optimization methods used for determining the geometry of shielding electrodes

The problem considered is that of determining the optimum profile and location of shielding for high-voltage equipment. The aim is to obtain a linear voltage distribution along the axis of symmetry. The calculation of electrostatic fields requires the solution of Laplace´s or Poisson´s equation with boundary conditions satisfied. The problem can be solved either by analytical or numerical methods such as the finite-difference technique, the finite-element method, the Monte Carlo method, and the charge simulation method. The latter is very simple when applied to the proposed system. It is shown that the use of the charge simulation for the determination of the optimum geometry of the shielding electrodes leads to an unconstrained minimization problem. Some algorithms are discussed and computational results are presented