Parallel model order reduction based on block discrete Fourier transform and Krylov subspace for parametric systems

Abstract

This paper explores a time-domain parallel parametric model order reduction (PMOR) method for parametric systems based on the block discrete Fourier transform (DFT) and Krylov subspace. The proposed method is suitable for parametric systems with non-affine parametric dependence. With Taylor expansion, the expansion coefficients of the state variable are first obtained. Then, we show that the subspace spanned by the expansion coefficients belongs to a Krylov subspace. To speed up the PMOR process, a parallel strategy based on the block DFT and the structured matrices is proposed to compute the matrices involved in the Krylov subspace. This can avoid directly computing the inverse of the large-scale matrix. After that, the reduced parametric systems are constructed with the projection matrix obtained by the Arnoldi algorithm and orthonormalisation. Furthermore, we analyse the invertibility and the error estimations to guarantee the feasibility of the proposed PMOR method. Finally, the numerical experiments are given to demonstrate the effectiveness of the proposed method.