A compact basis for reliable fast frequency sweep via the reduced-basis method

Abstract

A reliable reduced-order model (ROM) for fast frequency sweep in time-harmonic Maxwell’s equations by means of the reduced-basis method is detailed. Taking frequency as a parameter, the electromagnetic field in microwave circuits does not arbitrarily vary as frequency changes, but evolves on a very low-dimensional manifold. Approximating this low-dimensional manifold by a low dimension subspace, namely, reduced-basis space, gives rise to an ROM for fast frequency sweep in microwave circuits. This avoids carrying out time-consuming finite-element analysis for each frequency in the band of interest. The behavior of the solutions to Maxwell’s equations as a function of the frequency parameter is studied and highlighted. As a result, a compact reduced-basis space for efficient model-order reduction is proposed. In this paper, the reduced-basis space is composed of two parts: 1) eigenmodes hit in the frequency band of interest, which form an orthogonal, fundamental set that describes the natural oscillating dynamics of the electromagnetic field and 2) whatever else electromagnetic fields, sampled in the frequency band of interest, that are needed to achieve convergence in the reduced-basis approximation. The reduced-basis method aims not only to find out a reduced-basis space in an efficient way, but also to certify the reliability of the approximation carried out. Emphasis is placed on a fast evaluation of the ROM error measure and on providing a reliable convergence criterion. This approach is applied to both narrowband resonating structures and wideband nonresonanting devices in order to show the capabilities of the method in real-life applications.