电磁学中参数化系统模型降阶的无inf-sup常数状态误差估计器
Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric Systems in Electromagnetics
AI总结：
本文提出了一种避免计算inf-sup常数的后验状态误差估计器，用于电磁学参数化系统的模型降阶，在谐振频率附近的微波设备上验证了其优于现有方法的精度和效率。
摘要：
本文详细介绍了用于电磁学中参数化分析的可靠模型降阶过程。重点在于验证降阶模型的精度。为此，提出了一种锐利的状态误差估计器。模型降阶的标准后验状态误差估计依赖于inf-sup常数。对于参数化系统，inf-sup常数依赖于参数。对于具有非常小或消失的inf-sup常数的系统，后验误差估计面临挑战，因为它与inf-sup常数成反比，导致相当无用、过于悲观的误差估计器。这类系统出现在电磁学中，因为inf-sup常数值在接近谐振频率的点处接近零，并最终消失。我们提出了一种避免计算inf-sup常数的新型后验状态误差估计器。将所提出的状态误差估计器与标准误差估计器和文献中最近提出的一种进行了比较。结果表明，我们提出的误差估计器优于这两种现有估计器。在现实生活中的微波设备上进行了数值实验，如窄带和宽带天线、两种类型的介质谐振器滤波器以及双模波导滤波器。这些例子展示了所提方法的能力和效率。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
