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

Bonin, Thomas; Faßbender, Heike; Soppa, Andreas; Zaeh, Michael F.

doi:10.1016/j.matcom.2015.08.017

Cited by 28 publications

(33 citation statements)

References 23 publications

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“…Therefore proper selection of multiple expansion points is important. Previous studies on multiple-point expansion are found in [1,12,13,20,26,29]. In [26], the expansion points are chosen such that the reduced-order model is locally optimal.…”

Section: For Moment-matching Methods the Matrices W V Are Construcmentioning

confidence: 99%

Somea posteriorierror bounds for reduced-order modelling of (non-)parametrized linear systems

2017

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Abstract. We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds.

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Section: For Moment-matching Methods the Matrices W V Are Construcmentioning

confidence: 99%

Somea posteriorierror bounds for reduced-order modelling of (non-)parametrized linear systems

2017

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“…For the purpose of comparison in this paper, the global EKSM (GEKSM) [62] is used in some of our numerical experiments. Global rational Krylov subspace approaches are considered in [35] in the context of model order reduction.…”

Section: Modificationsmentioning

confidence: 99%

A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems

Benner¹,

Bujanović²,

Kürschner³

et al. 2020

SIAM J. Sci. Comput.

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In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical understanding and efficient implementation of various competing algorithms. There are several goals of this manuscript: first, to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them. Second, to analyze and compare the main computational ingredients of these algorithms, to detect their strong points and their potential bottlenecks. And finally, to compare the effective implementations of all methods on a set of relevant benchmark examples, giving an indication of their relative performance. *

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“…As observed in Section 4.3.4 and Section 4.4, the plain moment matching approach is sufficient for our model. In the general case, an adaptive method, such as the one discussed in [60], may improve the approximation.…”

Section: Moment Matchingmentioning

confidence: 99%

A comparison of second-order model order reduction methods for an artificial fishtail

Saak

Siebelts

Werner

2019

At - Automatisierungstechnik

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In order to apply control theory in small autonomous vehicles, mathematical models with small numbers of states are required for using the limited computational power in embedded programming. In this paper, we consider an artificial fishtail as an example for a complex mechanical system with a second-order large-scale model, which is derived by using the finite element method. To meet the above limitations, the several hundreds of thousands of degrees of freedom need to be reduced to merely a handful of surrogate degrees of freedom. We seek to achieve this task by various second-order model order reduction methods. All methods are applied on the fishtail’s matrices and their results are evaluated and compared in the frequency domain as well as in the time domain.

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

Cited by 28 publications

References 23 publications

Somea posteriorierror bounds for reduced-order modelling of (non-)parametrized linear systems

Somea posteriorierror bounds for reduced-order modelling of (non-)parametrized linear systems

A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems

A comparison of second-order model order reduction methods for an artificial fishtail

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