Practical Determination of an Effective Reduced Order in a Model Order Reduction of Dynamic FEM via Krylov Subspace

Abstract

A model order reduction has been utilized as a booster of FEM, mainly in the design of micro-electromechanical system, by using orthogonal basis vectors of the Krylov subspace. However, there is no clear procedure to determine a n effective reduced order, which indicates the number of the orthogonal basis vectors, because of the lack of error definition. In this paper, a practical use of the model order reduction via Krylov subspace (KS-MOR) is proposed to simulate low frequency responses of structure dynamics accurately. One of the important approximation properties of KS-MOR is the Moment Matching (MM). The MM provides a certain accuracy of KS-MOR in frequency domain, but the accurate frequency range cannot be defined. Then, a stepwise iterative frequency response analysis is utilized to evaluate an effective reduced order before it is applied in the time transient analysis. In the frequency analysis, simple error estimation is performed to c heck the comparison between the KS-MOR results with different number of basis vectors. Fin ally, a couple of numerical example has been simulated to validate our proposed procedure.