A Refined Arnoldi Algorithm Based Krylov Subspace Technique for MEMS Model Order Reduction

Abstract:

A refined approach producing MEMS numerical macromodels is proposed in this paper by generating the iterative Krylov subspace using a refined Arnoldi algorithm, which can reduce the degrees of freedom of the original system equations described by the state space method. Projection of the original system matrix onto the Krylov subspace which is spanned by a refined Arnoldi algorithm is still based on the transfer function moment matching principle. The idea of the iterative version is to expect that a new initial vector will contain more and more information on the required eigenvectors that is called refined vector. The refined approach improves approximation accuracy of the system matrix eigenvalues equivalent to a more accurate approximation to the poles of the system transfer function, obtaining a more accurate reduced-order model. The clamped beam model and the FOM model are reduced order by classical Arnoldi and refined Arnoldi algorithm in numerical experiments. From the computing result it is concluded that the refined Arnoldi algorithm based Krylov subspace technique for MEMS model order reduction has more accuracy and reaches lower order number of reduced order model than the classical Arnoldi process.

• Periodical: Key Engineering Materials (Volume 503)
• Pages: 260-265
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.503.260
• Online since: February 2012
• Authors: Le Guan, Jia Li Gao, Zhi Wen Wang, Guo Qing Zhang, Jin Kui Chu
• Keywords: Krylov Subspace, MEMS, Model Order Reduction, Refined Arnoldi Algorithm

References

[1] E. J. Grimme. Krylov projection methods for model reduction. Urbana-Champaign: University of Illinois, (1997).

[2] W. E. Arnoldi. The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart Appl Math. 9(1951)17-29.

DOI: 10.1090/qam/42792

[3] R. W. Freund. Krylov-subspace methods for reduced-order modeling in circuit simulation, J. Comput. Appl. Math, 123(2000)395-421.

DOI: 10.1016/s0377-0427(00)00396-4

[4] Z. X. Jia. Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems, Linear Algebra Appl. 259(1997)1-23.

DOI: 10.1016/s0024-3795(96)00238-8

[5] Z. X. Jia. A refined subspace iteration algorithm for large sparse eigenproblems, Appl. Numer. Math. 32(2000)35-52.

DOI: 10.1016/s0168-9274(99)00008-2

[6] R. B. Lehoucq, D. C. Sorensen. Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. &Appl. 17(1996)789-821.

DOI: 10.1137/s0895479895281484

[7] A. C. Antoulas, D. C. Sorenson, S. Gugercin. A survey of model reduction methods for Large-Scale systems, Contemp Math. 280(2001)193-219.