Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric Systems in Electromagnetics

TL;DR

This paper introduces a new state error estimator for parametric electromagnetics models that does not depend on the inf-sup constant, improving accuracy near resonant frequencies.

Contribution

A novel a posteriori state error estimator is proposed that avoids calculating the inf-sup constant, outperforming existing estimators in electromagnetics model reduction.

Findings

The new estimator outperforms existing methods in accuracy.

Numerical experiments on microwave devices validate the approach.

Method is effective near resonant frequencies with small or vanishing inf-sup constants.

Abstract

A reliable model order reduction process for parametric analysis in electromagnetics is detailed. Special emphasis is placed on certifying the accuracy of the reduced-order model. For this purpose, a sharp state error estimator is proposed. Standard a posteriori state error estimation for model order reduction relies on the inf-sup constant. For parametric systems, the inf-sup constant is parameter-dependent. The a posteriori error estimation for systems with very small or vanishing inf-sup constant poses a challenge, since it is inversely proportional to the inf-sup constant, resulting in rather useless, overly pessimistic error estimators. Such systems appear in electromagnetics since the inf-sup constant values are close to zero at points close to resonant frequencies, where they eventually vanish. We propose a novel a posteriori state error estimator which avoids the calculation of the inf-sup constant. The proposed state error estimator is compared with the standard error estimator and a recently proposed one in the literature. It is shown that our proposed error estimator outperforms both existing estimators. Numerical experiments are performed on real-life microwave devices such as narrowband and wideband antennas, two types of dielectric resonator filters as well as a dual-mode waveguide filter. These examples show the capabilities and efficiency of the proposed methodology.