Model order reduction for large systems in computational electromagnetics

This paper examines classical Model Order Reduction (MOR) strategies in view of the particular properties and needs of computational electromagnetism. Hereby reduced models are mainly needed for two reasons: The fast calculation of certain characteristics such as the transfer behavior over a range of excitation frequencies—especially for highly resonant systems—and the generation of macromodels such as equivalent circuits simplifying coupled simulations. In the first case, the computational cost of the method is of main interest, while in the second one the size of the reduced model as well as the conservation of stability and passivity plays a major role. The considered methods—partial realization, moment matching and modal extraction—are well-known and have been investigated for about two decades now. However, their efficiency appears in a different light if the number of unknowns reaches hundreds of thousands or even millions. This paper compares the suitability and efficiency of the mentioned methods for lossless or weakly lossy structures discretized by the Finite Integration Theory (FIT). Close relations and even transitions between the algorithms are shown. Finally, some specific properties of FIT enable the application of a method called Two-Step Lanczos (TSL): a successive application of partial realization and moment matching which is highly efficient in both computation time and model size, while preserving the passivity of the reduced models. TSL allows to compute the broadband transfer behavior of systems with hundreds of thousands of unknowns within minutes on a standard PC. Additionally, the resulting model can easily be implemented as a physical electric equivalent circuit.