Model Reduction for Mechanical Systems
Mechanical Models often feature vibrational analysis as the main investigation of interest. Therefore, the models treated here are usually of second differential order, which makes most standard MOR techniques only indirectly applicable, and usually the reduced order models are then of first order. Especially when a second order reduced model is required, or prefered for the subsequent investigations, special techniques need to be invesitgated and new efficient solvers for the reduction algorithms need to be developed.
Matrix equations of the one kind or the other are a central tool in all kinds of applications. In optimal control the linear quadratic control problem features a feedback solution that is determined via the solution of an algebraic Riccati equation. The system Gramians of a linear time invariant dynamical system are the solutions of two adjoint Lyapunov equations. Riccati, Lyapunov and Sylvester equations play an important role in different model order reduction techniques for continuous time linear dynamical systems. They all have discrete time counterparts as e.g. the well known Stein equations. Krylov subspace and eigenvalue methods can be related to certain Sylvester equations, as well.