Convergence enhancement for the vector finite element modeling of microwaves and antennas via differential evolution

A global optimization technique, based on the differential evolution algorithm is introduced to trace the optimal higher-order Whitney element, with respect to convergence, among a very wide class of parameter-dependent finite elements. Any tetrahedral element of this class provides exactly the same solution, but the convergence of the iterative solution method may significantly vary. Through the proposed comprehensive optimization procedure, the existence of optimal vector finite elements is revealed. The proposed method has been applied to obtain second-order elements utilized in three-dimensional microwave and antenna simulations.