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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 (ROM) with respect to the original full-order model (FOM) in an effective and efficient way. Previous works on model order reduction (MOR) accuracy certification rely on costly a posteriori error estimators, which typically require expensive inf-sup constant evaluations of the underlying FOM. 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 the 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 ROM state error in the frequency band of analysis, minimizing the number of FOM 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. [ABSTRACT FROM AUTHOR]

Efficient error estimation is important for reliable reduced-order modeling with guaranteed accuracy. We propose an error estimator for reduced-order modeling of linear parametric dynamical systems. The error estimator estimates the error of the reduced transfer function in the frequency domain and can be easily extended to the output error estimation of the reduced-order models (ROMs) for linear steady parametric systems. It is tight and cheap to compute. Using the error estimator, the ROM can be adaptively obtained with high reliability. Numerical results show that the error estimator can accurately estimate the true error even for transfer functions with many resonances. Compared with an existing error bound, the proposed error estimator can be orders of magnitudes sharper and needs much less computational time. [ABSTRACT FROM AUTHOR]

A fully adaptive model order reduction scheme based on moment matching is proposed to derive the reduced-order models of linear time-invariant (LTI) systems. According to the given error tolerance, the order of the reduced-order model as well as the expansion points for the transfer function is automatically determined on the fly during the process of model reduction. In this sense, the reduced-order model is automatically obtained without assigning the number of moments and expansion points in a priori, which is a prerequisite for the standard implementation of model reduction based on moment matching. The proposed adaptive scheme is found to be efficient when it is tested on various LTI systems. [ABSTRACT FROM AUTHOR]

Compact thermal models are often used during joint electrothermal simulation of microelectromechanical systems (MEMS) and circuits. Formal model reduction allows generation of compact thermal models automatically from high-dimensional finite-element models. Unfortunately, it requires fixing a film coefficient employed to describe the convection boundary conditions. As a result, compact models produced by model reduction do not comply with the requirements of being boundary condition independent. In the present paper, the authors suggest an approach of successive series expansion with respect to the film coefficient as well as to the frequency during model reduction that allows to overcome the problem and keep the film coefficient as a symbolic parameter in the reduced model. The approach is justified with a numerical example of electrothermal simulation of a microthruster unit. [ABSTRACT FROM AUTHOR]