Fast Frequency Sweep of FEM Models via the Balanced Truncation Proper Orthogonal Decomposition

A fast frequency sweep method for wideband antennas and infinite arrays based on a singular value decomposition (SVD)-Krylov model reduction method for frequency-domain tangential vector finite elements (TVFEMs) is presented. Reduced models are constructed using balanced congruence transformations constructed from the dominant invariant subspace of the system's Hankel matrix. Traditionally, forming such matrix requires the intensive computation of Gramians; the proposed method only forms their low-rank Cholesky factors via a novel adaptive proper orthogonal decomposition (POD) sampling strategy, leading to significant savings. Unlike some other model reduction methods, balanced truncation POD (BT-POD) is directly applicable to lossy and dispersive electromagnetic models. Numerical studies on large-scale wideband antennas and infinite arrays show that the method is stable, error controllable and, without memory overheads capable of up to two orders-of-magnitude speed-ups.