A Structured Quasi-Arnoldi procedure for model order reduction of second-order systems

Existing Krylov subspace-based structure-preserving model order reduction methods for the second-order systems proceed in two stages. The first stage is to generate a basis matrix of the underlying Krylov subspace. The second stage is to employ an explicit subspace projection to obtain a reduced-order model with a moment-matching property. An open problem is how to avoid explicit projection so that it will be efficient for truly large scale systems. In addition, it is also desired that a structure-preserving reduced system of order n matches maximum 2n moments.In this paper we propose a new procedure to compute a so-called Structured Quasi-Arnoldi (SQA) decomposition. Once the SQA decomposition is computed, a structure-preserving reduced-order model can be defined immediately from the decomposition without the explicit subspace projection. Furthermore, the reduced model of order n matches maximum 2n moments. Numerical examples demonstrate that the transpose-free SQA-based reduced model is compatible with the two-sided structure-preserving explicit projection methods and is more accurate than the one-sided structure-preserving explicit projection methods due to the higher number of matched moments.