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 kth-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 kth-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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.