Physics-Based Greedy Algorithm for Reliable Fast Frequency Sweep in Electromagnetics via the Reduced-Basis Method

Abstract

A reliable fast frequency sweep model order reduction (MOR) process is detailed. A reduced-basis approximation is taken into account to accurately and efficiently describe the electromagnetic field in a frequency band of analysis. The reduced-basis space is made up of snapshots of the electric field adaptively chosen on a physics-based greedy algorithm. Following a theoretical analysis starting from time-harmonic Maxwell’s equations, in- band eigenresonances are shown to significantly contribute to the electric field in the band of analysis. An impedance matrix transfer function description of the microwave circuit is used and a pole-residue expansion of this matrix-valued impedance transfer function is detailed. A fundamental physical property is identified, from which a straightforward a posteriori error estimator arises, namely, matrix residues in the pole-residue expansion of the impedance transfer function must be rank-1. This cheap computation is well-suited for fast greedy algorithm strategies in adaptive construction of the reduced-basis approximation. Contrary to what has been previously done, a straightforward physics-based greedy algorithm that does not need to scan the whole frequency band of interest to enrich the reduced-basis approximation is proposed. Finally, actual microwave applications illustrate the capabilities and efficiency of the new physics-based a posteriori error estimator in the proposed methodology.