Adaptive frequency‐limited ‐model order reduction

Abstract

AbstractIn this paper, we present an adaptive framework for constructing a pseudo‐optimal reduced model for the frequency‐limited ‐optimal model order reduction problem. We show that the frequency‐limited pseudo‐optimal reduced‐order model has an inherent property of monotonic decay in error if the interpolation points and tangential directions are selected appropriately. We also show that this property can be used to make an automatic selection of the order of the reduced model for an allowable tolerance in error. The proposed algorithm adaptively increases the order of the reduced model such that the frequency‐limited ‐norm error decays monotonically irrespective of the choice of interpolation points and tangential directions. The stability of the reduced‐order model is also guaranteed. Additionally, it also generates the approximations of the frequency‐limited system Gramians that monotonically approach the original solution. Further, we show that the low‐rank alternating direction implicit iteration method for solving large‐scale frequency‐limited Lyapunov equations implicitly performs frequency‐limited pseudo‐optimal model order reduction. We consider two numerical examples to validate the theory presented in the paper.