Reduced basis approximations in microwave filters and diplexers: Inf-sup constant behavior

Abstract

In this work, a model order reduction technique for fast frequency sweep in microwave filters and diplexers via the Reduced Basis Method is detailed. The Finite Element Method is used to solve the time-harmonic Maxwell's equations in these resonant circuit problems. Taking into account the electromagnetic field varies smoothly as a function of the frequency parameter, a low dimension system parameter manifold is identified. Thus, the original frequency-dependent Finite Element problem can be approximated by a model of reduced size using a Reduced Basis approximation. Based on the field frequency behavior in these resonant structures, the Reduced Basis space where the approximation holds is identified and characterized. Finally, special emphasis is placed in the behavior of the inf-sup constant used to provide an a posteriori error estimator, and its consequences in the Reduced Basis approximation are highlighted.