Order reduction of large scale second-order systems using Krylov subspace methods

By Behnam Salimbahrami, Boris Lohmann. 2006

230 citations recorded by the source corpus.

In order reduction of large-scale linear time invariant systems, Krylov subspace methods based on moment matching are among the best choices today. However, in many technical fields, models typically consist of sets of second-order differential equations, and Krylov subspace methods cannot directly be applied. Two methods for solving this problem are presented in this paper: (1) an approach by Su and Craig is generalized and the number of matching moments is increased; (2) a new approach via first-order models is presented, resulting in an even higher number of matching moments. Both solutions preserve the specific structure of the second-order type model.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/91662085a6fc8a89c94810c603d772daace4eff8

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In Computational Theory and Mathematics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

New advances in the forced response computation of periodic structures using the wave finite element (WFE) method (2014, background): “Such an issue is not new as already treated in various ways to address FRFs issued from matrix systems that are either linear or quadratic with respect to the frequency [3,8,20].”
On the use of modal derivatives for nonlinear model order reduction (2016, methodology): “Alternative methods that could also be used to derive a nonlinear reduced-order model are so-called moment matching [39] or Krylov subspace methods [40] for nonlinear systems.”
Parametric Order Reduction of Proportionally Damped Second Order Systems (2006, methodology): “Also, special model reduction methods based on the so called Second Order Krylov Subspaces have been developed to treat second order systems directly [3, 11, 15, 16].”
Simulation process of flexible multibody systems with non-modal model order reduction techniques (2011, methodology): “Momentmatching for second-order systems can be achieved by projection on a second-order Krylovsubspace [20].”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, background): “MOR on second order systems is discussed e.g. in [18,39,71,174,186,203].”
Balanced truncation model reduction of second-order systems (2008, methodology): “Two different modifications of this approach have been proposed for second-order systems [3, 12–14, 16, 17].”