Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method

A structure-preserving dimension reduction algorithm for large-scale second-order dynamical systems is presented. It is a projection method based on a second-order Krylov subspace. A second-order Arnoldi (SOAR) method is used to generate an orthonormal basis of the projection subspace. The reduced system not only preserves the second-order structure but also has the same order of approximation as the standard Arnoldi-based Krylov subspace method via linearization. The superior numerical properties of the SOAR-based method are demonstrated by examples from structural dynamics and microelectromechanical systems.