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Subspace recycling accelerates the parametric macro-modeling of MEMS

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  • This is a considerably extended version of the paper ‘Parametric Model Order Reduction Accelerated by Subspace Recycling’, presented at the joint 48th IEEE Conference on Decision Control and 28th Chinese Control Conference, Shanghai, PR China, December 16–18, 2009 [1].

Correspondence to: Lihong Feng, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.

E-mail: feng@mpi-magdeburg.mpg.de

SUMMARY

A fast computational technique that speeds up the process of parametric macro-model extraction is proposed. An efficient starting point is the technique of parametric model order reduction (PMOR). The key step in PMOR is the computation of a projection matrix V, which requires the computation of multiple moment matrices of the underlying system. In turn, for each moment matrix, a linear system with multiple right-hand sides has to be solved. Usually, a considerable number of linear systems must be solved when the system includes more than two free parameters. If the original system is of very large size, the linear solution step is computationally expensive. In this paper, the subspace recycling algorithm outer generalized conjugate residual method combined with generalized minimal residual method with deflated restarting (GCRO-DR), is considered as a basis to solve the sequence of linear systems. In particular, two more efficient recycling algorithms, G-DRvar1 and G-DRvar2, are proposed. Theoretical analysis and simulation results show that both the GCRO-DR method and its variants G-DRvar1 and G-DRvar2 are very efficient when compared with the standard solvers. Furthermore, the presented algorithms overcome the bottleneck of a recently proposed subspace recycling method the modified Krylov recycling generalized minimal residual method. From these subspace recycling algorithms, a PMOR process for macro-model extraction can be significantly accelerated. Copyright © 2013 John Wiley & Sons, Ltd.

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