On parametric model order reduction by matrix interpolation

Abstract

A general framework for model order reduction is proposed for high-order parameter-dependent, linear time-invariant systems. The procedure is based on matrix interpolation and consists of six steps. At first a set of high-order nonparametric systems is computed for different parameter vectors. The resulting local high-order systems are then reduced by a projection-based reduction method. Thereby, proper right and left subspaces for the reduced systems are calculated. Next the bases of the right subspaces of the reduced systems are adapted and the bases of the left subspaces are adjusted. For that the concept of duality is introduced. Finally, the precomputed matrices of the local systems are interpolated in a matrix manifold with an interpolation method. In this paper the six steps of the algorithm and the degrees of freedom which arise therein are presented. Furthermore, advantages and difficulties in the selection of the degrees of freedom are pointed out. It is additionally shown that two existing methods for parametric model order reduction by matrix interpolation are special cases of the proposed general procedure as they - often implicitly - determine a limiting selection of the degrees of freedom.