Fast A Posteriori State Error Estimation for Reliable Frequency Sweeping in Microwave Circuits via the Reduced-Basis Method

TL;DR

This paper introduces a fast, reliable reduced-basis method for frequency sweeps in microwave circuits, emphasizing efficient error certification for the full electric field state to ensure model accuracy.

Contribution

It presents a novel approach to certify reduced-order model accuracy efficiently by focusing on electric field error estimation, reducing the need for costly full-order evaluations.

Findings

Effective frequency-dependent electric field error estimation

Significant reduction in full-order model evaluations

Reliable and fast frequency sweep capability

Abstract

We develop a compact, reliable model order reduction approach for fast frequency sweeps in microwave circuits by means of the reduced-basis method. Contrary to what has been previously done, special emphasis is placed on certifying the accuracy of the reduced-order model with respect to the original full-order model in an effective and efficient way. Previous works on model order reduction accuracy certification rely on costly $\textit{a posteriori}$ error estimators, which typically require expensive $\textit{inf-sup}$ constant evaluations of the underlying full-order model. This scenario is often too time-consuming and unaffordable in electromagnetic applications. As a result, less expensive and heuristic error estimators are commonly used instead. Very often, one is interested in knowing about the full state vector, instead of just some output quantities derived from the full state. Therefore, error estimators for the full state vector become relevant. In this work, we detail the frequency behavior of both the electric field and the state error when an approximation to the electric field solution is carried out. Both field quantities share the same frequency behavior. Based on this observation, we focus on the efficient estimation of the electric field state error and propose a fast evaluation of the reduced-order model state error in the frequency band of analysis, minimizing the number of full-order model evaluations. This methodology is of paramount importance to carry out a reliable fast frequency sweep in microwave circuits. Finally, real-life applications will illustrate the capabilities and efficiency of the proposed approach.