Adaptive-order rational Arnoldi-type methods in computational electromagnetism

Bodendiek, André; Bollhöfer, Matthias

doi:10.1007/s10543-013-0458-9

Cited by 16 publications

(27 citation statements)

References 38 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%

“…In [26], the expansion points are chosen such that the reduced-order model is locally optimal. A binary search is used in [1,12,20] for adaptive, but heuristic selection of the expansion points. In Section 7.2, we readdress the problem of selecting multiple expansion points by using the global a posteriori error bounds proposed in Section 3 and Section 4.…”

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

confidence: 99%

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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%

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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“…The expansion points have been determined adaptively on the basis of the rational Krylov residual, see [2]. In general, the numerical experiments indicate that the computational effort for the subsequent calls of the mAORA method reduces about a factor of three.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A modified adaptive‐order rational Arnoldi method for model order reduction

Bodendiek

Bollhöfer

2013

Proc Appl Math and Mech

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A Greedy-type expansion point selection for moment-matching methods in model order reduction mainly depends on the computation of a sequence of reduced order models. Typically, the adaptive-order rational Arnoldi (AORA) method resembles an efficient way for the computation of a Galerkin projection corresponding to a set of expansion points. We will provide an extension of the AORA method, in order to reuse the orthonormal basis from previous calls of the AORA method.

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“…In [7,22] Gugercin et al proposed an Iterative Rational Krylov Algorithm (IRKA) to compute a reduced order model satisfying the firstorder conditions for the H 2 approximation. Other adaptive methods (for the SISO case) are introduced in [9,19,20,25,27,30] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems

2015

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Mathematical modeling of complex electrical systems, has led us to linear mathematical models of higher order. Consequently, it is difficult to analyse and to design a control strategy of these systems. The order reduction is an important and effective tool to facilitate the handling and designing of a control strategy. In this paper we present, firstly, a reduction method which is based on the Krylov subspace and Lyapunov techniques, that we call Lyapunov-Global-Lanczos. This method minimizes the H∞ norm error, absolute error and preserves the stability of the reduced system. It also provides a better reduced system of order 1, with closer behaviour to the original system. This first order system is used to design PI (Proportional-Integral) controller. Secondly, we implement an adaptive digital PI controller in a microcontroller. It calculates the PI parameters in real time, referring to the error between the desired and measured outputs and the initial values of PI controller, that were determined from the first order system. Two simulation examples and a real time experimentation are presented to show the effectiveness of the proposed algorithms.

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Adaptive-order rational Arnoldi-type methods in computational electromagnetism

Cited by 16 publications

References 38 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 modified adaptive‐order rational Arnoldi method for model order reduction

An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems

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