Krylov Acceleration Techniques for Time-Reversal Design Applications

Time-reversal approaches provide a simple design optimization procedure for a class of electromagnetic components. The approach comprises iterations of forward and reverse time simulations that can be undertaken using any numerical time-domain algorithm. However, although this offers significant flexibility, it is computationally intensive, and therefore, it is important to increase the convergence rate of the method. In this work, the physically based time-reversal iterations are accelerated using Krylov subspace methods, which are shown to provide a valuable improvement in computational efficiency. Two illustrations are presented: waveguide filters and impedance matching a waveguide bend, and both stationary and nonstationary linear acceleration methods are considered, employing the time-stepping transmission-line modeling method to perform the necessary simulations.