Model order reduction in parallel of discrete-time linear systems based on Meixner and Krawtchouk polynomials

Author:

Xu Kang-Li1,Li Zhen2,Jiang Yao-Lin1,Li Li3

Affiliation:

1. School of Mathematics and Statistics , Xi’an Jiaotong University, 710049 Xi’an , P R China

2. College of Computer Science and Technology , Xi’an University of Science and Technology, 710054 Xi’an , P R China

3. AVIC Aeronautical Laboratory of Computational Fluid Dynamics , Xi’an Aeronautics Computing Technique Research Institute, Xi’an 710068 , P R China

Abstract

Abstract In this paper, based on the partition technique, we use Meixner and Krawtchouk polynomials to present an input-independent model order reduction method. Our main contributions are twofold. First, the explicit difference relations of Meixner polynomials and Krawtchouk polynomials are expressed in an unified form. The parallel computation is carried out on the partitioned subsystems using the Krylov subspaces by which one can generate reduced systems independent of the expansion coefficients of input and can save the computation time. Second, a parallel adaptive enrichment strategy is used to choose the reduced order of reduced systems. Theoretical analysis shows that the proposed method characterizes the property of invariable coefficients. Finally, two numerical examples demonstrate that the proposed method achieves good reduction results in terms of accuracy and reduced CPU time.

Funder

Natural Science Foundation of China

Aviation Science Foundation Project

China Postdoctoral Science Foundation

Shaanxi Fundamental Science Research Project for Mathematics and Physics

Fundamental Research Funds for the Central Universities

Publisher

Oxford University Press (OUP)

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5. Special Functions

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