A multi-point parameterized model reduction for large parametric systems by using Krylov-subspace techniques

Abstract

This paper presents a multi-point parameterized model reduction method based on Krylov-subspace techniques for large parametric systems where the parametric dependence in system matrices can be nonaffine and the parameters are in a wide range. First, a large parametric system is approximated as a weighted combination of different linear parametric systems, which are obtained by Taylor expansion on the different selected parameter expansion points. Then, a numerically stable algorithm based on self-moments and cross-moments is proposed to obtain a reduced parametric system with high fidelity in the full ranges of the parameters. The accuracy of the obtained reduced parametric systems can be improved by applying the multi-point expansions and weighted functions proposed in this paper. Two benchmarks in practical applications are assessed by employing different parameterized model reduction methods. The numerical simulation results verify the effectiveness of the proposed method.