Discretization and Model Reduction Error Estimation of Interconnected Dynamical Systems

Abstract

In this paper a novel approach for estimating both discretization and model order reduction error is presented. Discretization is carried out using finite element method. Finite element models are converted to linear time-invariant state space models. Using the generalized square root balanced truncation method a series of reduced models are obtained. It is shown that for special class of passive and dissipative dynamical systems upper a-posteriori reduction error bound can be modeled less conservatively. Estimation of both discretization and model reduction error is further refined using v-gap metric. Quality of the obtained reduced order model is verified in the frequency domain. The proposed error estimation approach is demonstrated on a numerical example.