INVERSE PROBLEMS WITH BOUNDARY ELEMENTS - SYNTHESIZING A CAPACITOR

As the solution of direct electromagnetic field problems is increasingly satisfactorily addressed, recent research has turned to the use of inverse problem methodology in the synthesis of engineering devices. The gradient methods have been effectively used with the finite element method, using the ease with which finite element solution's derivative with respect to design parameters is obtained. In this paper, we show how the boundary element solution too, may be differentiated with respect to a design parameter without having to solve a second perturbed field problem. We show 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 a fringing capacitor.