Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations

Abstract

The reduced basis method (RBM) generates low-order models of parametrized partial differential equations. These allow for the efficient evaluation of parametrized models in many-query and real-time contexts. We use the RBM to generate low-order models of microscale models under variation of frequency, geometry, and material parameters. In particular, we focus on the efficient estimation of the discrete stability constant used in the reduced basis error estimation. A good estimation of the discrete stability constant is a challenging problem for Maxwell's equations, but is needed to yield rigorous bounds on the model approximation error. We therefore test and compare multiple techniques and discuss their properties in this context.