Inverse problems with boundary elements: synthesizing a capacitor

A methodology for the solution of inverse problems in electromagnetics using boundary element analysis is developed. It is shown how the boundary element solution may be differentiated with respect to a design parameter without having to solve a second perturbed field problem. It is demonstrated that the small, full nature of the boundary element coefficient matrix makes the method cost-effective compared to the finite element method, in obtaining the gradient of the solution, since matrix decomposition is the preferred method of solution with boundary elements. The theory propounded here is demonstrated on the optimization of fringing capacitor.>