A strong adaptive piecewise model order reduction method for large-scale dynamical systems with viscoelastic damping. (1st February 2022) - Tao, Tianzeng; Zhao, Guozhong; Zhai, Jingjuan; Ren, Shanhong
Highlights: Frequency-dependent system is piecewise treated via polynomial least squares approximations. The reasonable initial order and order increment are determined adaptively. The forms of estimated relative errors are predicted and studied in advance. The present PMOR method allows for a significant speedup in solving large-scale dynamical with viscoelastic damping. Abstract: This paper develops a novel and strong adaptive piecewise model order reduction (PMOR) method for large-scale dynamical systems with viscoelastic damping. Based on polynomial least squares approximations, the system is piecewise approximated by several k t h -order ( k ≥ 2 ) dynamical systems in a wide target frequency band, in which the orders are adaptively determined with a curvature-based method. Then the convergent reduced-order models (ROMs) of the approximate systems are obtained gradually. In the above process, for each approximate system, the orthonormal basis is constructed iteratively via the k t h -order Arnoldi method to span a projection subspace. To accelerate the convergence, an influence coefficient method and an order-dependent method are proposed to automatically determine the initial order of the ROM and the order increments, respectively. More importantly, a proposed error estimation strategy can predict all forms of estimated relative errors. According to the study of these forms, a comparison-selection method is presented to determine the final ROM for the whole target band interval by interval. Four examples comprehensively validate the strong adaptive ability, high efficiency and wide applicability of the PMOR method.