Optimal design of electrostatic lenses using integral equation field methods

The integral method of solving Laplace's or Poisson's equation results in a formulation for solution which is suitable for directly calculating the change in the domain potentials due to displacing the domain boundaries. Specifically, the order and locations remain the same for the matrix ∂Φ/∂x i.e., the change in potential per boundary change, which is required for the optimum design problem.