A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping

The model order reduction of second-order dynamical multi-input and multi-output (MIMO) systems with proportional damping arising in the numerical simulation of mechanical structures is discussed. Based on finite element modelling the systems describing the mechanical structures are large and sparse...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 122; pp. 1 - 19
Main Authors Bonin, Thomas, Faßbender, Heike, Soppa, Andreas, Zaeh, Michael
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2016
Subjects
Global Arnoldi algorithm
Krylov subspace
Model order reduction
Moment matching
Simulation
Model order reduction
Moment matching
Simulation
Krylov subspace
Global Arnoldi algorithm
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Summary:The model order reduction of second-order dynamical multi-input and multi-output (MIMO) systems with proportional damping arising in the numerical simulation of mechanical structures is discussed. Based on finite element modelling the systems describing the mechanical structures are large and sparse, either undamped or proportionally damped. This work concentrates on a new model reduction algorithm for such second order MIMO systems which automatically generates a reduced system approximating the transfer function in the lower range of frequencies. The method is based on the rational global Arnoldi method. It determines the expansion points iteratively. The reduced order and the number of moments matched per expansion point are determined adaptively using a heuristic based on some error estimation. Numerical examples comparing our results to modal reduction and reduction via the rational block Arnoldi method are presented.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2015.08.017