An Adaptive Method for Reducing Second-order Dynamical Systems

We present a method to compute reduced models of second-order dynamical systems valid in a desired frequency range without specifying the order of the reduced models prior to the reduction process. The approach is based on a second-order variant of the iterative rational Krylov algorithm (SO-IRKA) and exploits the fact, that an eigenvalue decomposition of the reduced second-order system yields twice as many eigenvalues as its order. By selecting all eigenvalues whose mirror images lie in the frequency range in which the reduced model should be valid during each iteration of SO-IRKA, the order of the reduced model is growing (or shrinking) until a reasonable reduced order is found. Additionally, we show that performing the SO-IRKA optimization steps on an intermediate-sized model yields accurate reduced-order models while the computational cost of the reduction phase is reduced. We show the effectiveness of the proposed method by applying it to numerical models of a vibro-acoustic system.