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.

翻译：本文详细阐述了一种用于电磁学参数化分析的可靠模型降阶流程，特别强调了对降阶模型精度的认证。为此，提出了一种尖锐的状态误差估计器。标准模型降阶的后验状态误差估计依赖于inf-sup常数。对于参数化系统，inf-sup常数具有参数依赖性。当系统inf-sup常数非常小甚至消失时，标准后验误差估计面临挑战，因为其与inf-sup常数成反比，导致产生过于悲观且几乎无用的误差估计器。这类系统常见于电磁学中：在接近谐振频率的频点处，inf-sup常数值趋近于零并最终消失。我们提出了一种新型后验状态误差估计器，避免了对inf-sup常数的计算。将该估计器与标准估计器及近期文献提出的估计器进行了比较，结果表明我们的估计器优于这两种现有方法。通过对窄带和宽带天线、两种介质谐振滤波器以及双模波导滤波器等实际微波器件的数值实验，验证了所提方法的有效性与高效性。