Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

In this paper, a reduced-basis-approximation-based model-order reduction for fast and reliable frequency sweep in the time-harmonic Maxwell's equations is detailed. Contrary to what one may expect by observing the frequency response of different microwave circuits, the electromagnetic field within these devices does not drastically vary as frequency changes in a band of interest. Thus, instead of using computationally inefficient, large dimension, numerical approximations such as finite- or boundary-element methods for each frequency in the band, the point in here is to approximate the dynamics of the electromagnetic field itself as frequency changes. A much lower dimension, reduced-basis approximation sorts this problem out. Not only rapid frequency evaluation of the reduced-order model is carried out within this approach, but also special emphasis is placed on a fast determination of the error measure for each frequency in the band of interest. This certifies the accurate response of the reduced-order model. The same scheme allows us, in an offline stage, to adaptively select the basis functions in the reduced-basis approximation and automatically select the model-order reduction process whenever a preestablished accuracy is required throughout the band of interest. Finally, real-life applications will illustrate the capabilities of this approach.