A fast FEM-based field optimization using analytically calculated gradients

This paper describes an efficient gradient-based optimization algorithm for the FEM. In contrast to the standard approach, which uses a finite difference calculation to find the gradient of a cost function, the gradient is calculated analytically. Hence only a single FEM analysis is required and no mesh re-adjustment is necessary. This saves not only computer memory but reduces computer time significantly. The analytically calculated gradient is exact and singularities (like in the finite difference technique) do not occur. To illustrate the approach a simple H-plane filter is used heading