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.