Parametric Interpolation Model Order Reduction on Grassmann Manifolds by Parallelization

Abstract

Based on Riemannian geometry of Grassmann manifolds and discrete Laguerre polynomials, we propose a parametric interpolation parallel MOR method for discrete-time parametric systems. First, a block discrete Fourier transform-based (BDFT) parallel strategy is presented to construct the local basis matrices, which achieves two level acceleration by parallelization. Further, using the retractions and vector transports on Grassmann manifolds, the basis matrix for a new parameter is obtained by interpolating the local bases on the tangent spaces at the different reference points. Finally, a numerical example is used to demonstrate the efficiency of our method.