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A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors

PAMM 2013年第1期13卷

作者： Peter Benner Patrick Kürschner Jens Saak Max Planck Institute for Dynamics of Complex Technical Systems: Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg

Based on our recent findings [1, 2] regarding the low-rank ADI iteration for large-scale Lyapunov equations, we propose a mathematically equivalent formulation of the LR-ADI whose iteration is directly connected to low rank factors of the Lyapunov residual. If complex shift parameters occur and are handled efficiently [1], this reformulation is slightly more efficient from a computational point of view, since it guarantees that the right hand sides of all linear systems that need to be solved are real. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Bounds on the Solution of Linear Time-Periodic systems

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PAMM 2013年第1期13卷

作者： Peter Benner Jonas Denißen Ludwig Kohaupt Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Germany Beuth University of Applied Sciences Berlin Faculty II – Mathematics Luxemburger Straße 10 13353 Berlin Germany

Linear time-periodic systems have been an active area of research in the last decades. They arise in various applications such as anisotropic rotor-bearing systems and nonlinear systems linearized about a periodic trajectory. Rigorous bounds support the transient analysis of these systems. Optimal constants are determined by the differential calculus for norms of matrix functions. Bounds based on trigonometric spline approximations of the solution are introduced and convergence results for the approximations are stated. Bounds are illustrated by means of an anisotropic rotor-bearing system. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Avoiding complex arithmetic in the low-rank ADI method efficiently

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PAMM 2012年第1期12卷

作者： Peter Benner Patrick Kürschner Jens Saak Max Planck Institute for Dynamics of Complex Technical Systems: Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg

We present a new reformulation of the low-rank ADI method for solving large-scale Lyapunov equations which uses only real arithmetic operation and storage in the presence of complex shift parameters. This makes the method applicable on computing environments where complex computations and storage are not supported or not efficiently available. For generalized Lyapunov equations it is significantly more efficient than the older completely real formulation of the low-rank ADI as confirmed by numerical examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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On stability, passivity and reciprocity preservation of ESVDMOR

On stability, passivity and reciprocity preservation of ESVD...

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Workshop on Model Reduction for Circuit Simulation

作者： Benner, Peter Schneider, André Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Germany Technische Universität Chemnitz Fakultät für Mathematik 09107 Chemnitz Germany

ISBN: (纸本)9789400700888

The reduction of parasitic linear subcircuits is one of many issues in model order reduction (MOR) for VLSI design. This issue is well explored, but recently the incorporation of subcircuits from different modelling sources into the circuit model has led to new structural aspects: so far, the number of elements in the subcircuits was significantly larger than the number of connections to the whole circuit, the so called pins or terminals. This assumption is no longer valid in all cases such that the simulation of these circuits or rather the reduction of the model requires new methods. In Feldmann and Liu (ICCAD '04: Proceedings of the 2004 IEEE/ACM International Conference on Computer-Aided Design, 88-92, 2004), Liu et al. (ICCAD '05: Proceedings of the 2005 IEEE/ACM International Conference on Computer-Aided Design, 821-826, 2004;Integr. VLSI J. 41(2):210-218, 2008) the extended singular value decomposition based model order reduction (ESVDMOR) algorithm is introduced as a way to handle this kind of circuits with a massive number of terminals. Unfortunately, the ESVDMOR approach has some drawbacks because it uses the SVD for matrix factorizations. In Benner (Mathematics in Industry 14, 2009), Schneider (Matrix decomposition based approaches for model order reduction of linear systems with a large number of terminals, 2008) the truncated SVD (TSVD) as an alternative to the SVD within the ESVDMOR is introduced. In this paper we show that ESVDMOR as well as the modified approach is stability, passivity, and reciprocity preserving under reasonable assumptions. © 2011 Springer Science+Business Media B.V.

关键词： Singular value decomposition

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Robust Iterative Solution of a Class of Time-Dependent Optimal control Problems

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PAMM 2012年第1期12卷

作者： John W. Pearson Martin Stoll Andrew J. Wathen Numerical Analysis Group Mathematical Institute University of Oxford 24–29 St Giles' Oxford OX1 3LB UK Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg Germany

The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1, 1)-block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step-size and regularization parameter. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Two-sided harmonic subspace extractions for the generalized eigenvalue problem

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PAMM 2011年第1期11卷

作者： Peter Benner Michiel Hochstenbach Patrick Kürschner Max Planck Institute for Dynamics of Complex Technical Systems: Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Technische Universiteit Eindhoven: Centre for Analysis Scientific Computing and Applications Den Dolech 2 NL-5612 AZ Eindhoven

One crucial step of the solution of large-scale generalized eigenvalue problems with iterative subspace methods, e.g. Arnoldi, Jacobi-Davidson, is a projection of the original large-scale problem onto a low dimensional subspaces. Here we investigate two-sided methods, where approximate eigenvalues together with their right and left eigenvectors of the full-size problem are extracted from the resulting small eigenproblem. The two-sided Ritz-Galerkin projection can be seen as the most basic form of this approach. It usually provides a good convergence towards the extremal eigenvalues of the spectrum. For improving the convergence towards interior eigenvalues, we investigate two approaches based on harmonic subspace extractions for the generalized eigenvalue problem. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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On ℋ︁2-model reduction of linear parameter-varying systems

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PAMM 2011年第1期11卷

作者： Peter Benner Tobias Breiten Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Tobias Breiten phone +49 391 6110 474 fax +49 391 6110 500 Peter Benner phone +49 391 6110 451 fax +49 391 6110 453

In this paper, we will discuss an advantageous relation between a special class of linear parameter-varying systems and bilinear control systems. This will automatically lead to parameter-preserving model reduction techniques. Furthermore, we review a recently introduced interpolation-based ℋ 2 -framework for bilinear control systems. By means of a numerical example, the efficiency of the new method will be underlined. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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A Parallel Block Scaled Gradient Method With Decentralized Step-Size For Block Additive Unconstrained Optimization Problems Of Large Distributed systems

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Asian Journal of control 2008年第1期5卷

作者： Shin-Yeu Lin Shieh-Shing Lin Department of Electrical and Control Engineering National Chiao Tung University Hsinchu 30039 Taiwan. Shin-Yen Lin received the B.S. degree in electronic engineering from National Chiao Tung University the M.S. degree in electrical engineering from the University of Texas at E1 Paso and the D.Sc. degree in systems science and mathematics from Washington University in St. Louis Missouri in 1975 1979 and 1983 respectively. From 1991 to the present he has been a Professor in the Department of Electrical and Control Engineering at National Chiao Tung University. His major research interests are Computational Intelligence Optimization Theory and Applications and Large-scale Power Systems.

In this paper, we propose a modified parallel block scaled gradient method for solving block additive unconstrained optimization problems of large distributed systems. Our method makes two major modifications to the typical parallel block scaled gradient method: First, we include a pre-processing step which reduces the computational time; second, we propose a decentralized Armijo-type step-size rule. This rule circumvents the difficulty of determining a step-size in a distributed computing environment and enables the proposed parallel algorithm to execute in a distributed computer network with a limited amount of data transfer. We have applied our method to the weighted-least-square problems of power system state estimation and demonstrated the convergence of our method by testing numerous examples on a PC network. The speedup ratio of the distributed version of our method tends to increase proportionally with the number of subsystems (or computers).

关键词： Unconstrained optimization nonlinear programming parallel computation large distributed systems least-square problems

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Application of 3-D nonlinear wave-load and structural-response simulations in naval ship design

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NAVAL ENGINEERS JOURNAL 1997年第3期109卷 253-266页

作者： Engle, A Lin, W Salvesen, N Shin, Y Allen H. Engle:is a naval architect in the Hydrodynamic Division of the Naval Sea Systems /Command (NavSea). He received his B.S. degree in engineering scinece from the State University of New York at Buffalo in 1977 and his M.S. degree in ocean engineering from the Unviersity of Hawaii in 1979. Corrently Mr. Engle is the program director of the Navy's Hydrodynamic Loads Technology Development Program. Mr. Engle is Chairman of SNAME Panel on Hull Loadings (HS-1) and contributing member to the International Ship and Offshore Structures Congress's Committee on Dynamics. Moei-Min Lin:is a senior research scientist at the Ship technology Division of Sciences Applications International Corporation (SAIC). He received his B.S. degree in naval architecture and marine engineering from the National Cheng-Kung University Taiwan in 1977 and his Ph.D. degree in ocean engineering from MIT in 1985. He is an expert in computational ship hydrodynamics. He has been the P.I. for development of the Large Amplitude Motions Program (LAMP) system. Nils Salvesen:is the manager of the Ship Technology Division of the Science Application International Corporation (SAIC).He received his B.S. and Ph.D. degree from the Development Naval Architecture and Marine Engineering of the University of Michigan in 1960 and 1966 respectively. He has more then thirty years of experience in the development of ship motion simulation and wave load prediction methods. More than twenty-five years ago he developed the original strip-theory code on which the Navy's ship motions program (SMP) is based. Yung-Sup Shin:is the principal engineer responsible for the hydrodynamic projects in the Research and Development Department of the American Bureau of Shipping New York. He received a Ph.D. degree in hydrodynamic from the Department of Naval Architecture and Marine Engineering of the University of Michigan. In the past eighteen years at ABS he has been involved in the theortical development and analysis of various marine hydrodynamic problems. In recent year

Despite the limits inherent within linearized frequency-domain ship motion and wave load computer codes, strip theory has been found to provide the design community with a fairly robust, practical design tool with reasonable accuracy for most conventional displacement monohulls. However, the advent of new design concepts including multi-hulls and application of new materials as well as the push to incorporate reliability methods within surface ship structural design criteria has highlighted the need for more rigorous methods of developing a lifetime load spectrum. In this paper, a multilevel computation system for predicting ship motions and wave loads, up through and including extreme sea conditions, is presented. This system includes a traditional strip theory approach and newly developed linear and nonlinear three-dimensional time-domain methods. The new nonlinear methods are currently in the process of being validated by the U.S. Navy. The status of the current development is presented. Sample numerical results from the new nonlinear methods are compared with both linear frequency domain predictions and model tests.

关键词： Naval vessels

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Steady‐state security evaluation of electrical power systems by means of artificial neural network

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European Transactions on Electrical Power 1995年第2期5卷 91-97页

作者： Chiodo, E. Menniti, D. Testa, A. Picardi, C. Elio Chiodo (1959) received the degree in Electronics Engineering in 1985 and the Ph.D. degree in Computational Statistics both from the University of Naplefltaly. He is a Researcher at the Department of Electrical Engineering of the University of Naples and a member of the Italian Statistical Society. His areas of interest include probabilistic methods applied to electric power systems analysis. (University of Naples Fedrrico 11. Electrical Engineering Dept.via Claudio 21 1-80125 Naplefltaly T +3981/7683226 Fax+3981/2396897) Daniele Menniti (1958) received the degree in Electrical Engineering from the University of Calabria. Cosenzataly and the Ph.D. degree in Electrical Engineering from the University of NapleslItaly in 1984 and 1989 respectively. He is a researcher at the Electronic. Computer and Systems Science Department of the University of Calabria. Italy. Hiscurrent research interests concern electric power system analysis real-time control and automation. (University of Calabria Electronic Computer and Systems Science Dep. Arcavacataji Rende (CS). 1-87036 CosenzdItaly T +39984/494707. Fax +39984/4947 13) Alfredo Testa (1950) received the degree in Electrical Engineering from the University of Naples/Italy in 1975. He is an Associate Professor in Electrical Power Systems at the Department of Electrical Engineering of the University of Naples. He is engaged in researches on electrical power systems reliability and harmonic analysis. (University of Naples Federico 11. Electrical Engineering Dep. via Claudio '2 1 1-80 I25 NapleslItaly T + 39 8 I/7 68 3'2 11. Fax+3981/2396897) Ciro Picardi (1949) received the degree in Electronics Engineering from the University of Naples/Italy in 1975. He is currently Associate Professor in Process Control at the Department of Electronic Computer and System Science of the University of Calabria. Italy. His current research interests are in the area of electrical drives robotics neural networks and fuzzy control. (University of Calabria Electronic. Compu

An artificial‐neural‐network (ANN) application for steady‐state security evaluation of electrical power systems is presented. Such application is based upon a combined use of a multilayer back‐propagation neural network and of an opportune electrical system model, previously proposed by some of the authors. In the paper, the definition of steady‐state security and the problems arising from its on‐line evaluation are briefly recalled. Then, the ANN utilized is described with particular reference to the solutions adopted by the authors. Afterwards, some remarks on the system model utilized are reported. Finally, numerical applications on the AEP‐14 bus system are presented and the results obtained with different ANN configurations are analyzed. Copyright © 1995 John Wiley & Sons, Ltd.

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