Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems

Abstract

In recent years, a great deal of attention has been devoted to Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. The surge of interest was triggered by the pressing need for efficient numerical techniques for simulations of extremely large-scale dynamical systems arising from circuit simulation, structural dynamics, and microelectromechanical systems. In this paper, we begin with a tutorial of a Lanczos process based Krylov subspace technique for reduced-order modeling of linear dynamical systems, and then give an overview of the recent progress in other Krylov subspace techniques for a variety of dynamical systems, including second-order and nonlinear systems. Case studies arising from circuit simulation, structural dynamics and microelectromechanical systems are presented.