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IEEE Topical Meeting on Electrical Performance of Electronic Packaging (EPEPS)

作者： G. De Luca G. Antonini P. Benner Dipartimento di Ingegneria Industriale e dell' Informazione e di Economia Universita' degli Studi dell'Aquila L'Aquila Italy Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

This paper describes a model order reduction technique for circuit simulation, based on the parallelization of the well-known multi-point PRIMA algorithm. In order to obtain an optimal accuracy of the reduced-order model in the entire frequency range of interest, the reduced models are computed on different expansion points in correspondence of which the errors, between the transfer functions of the original model and of the actual reduced one, exhibit the largest value, in a recursive way. Moreover, since the computation of the error is a computationally expensive routine, this task is parallelized, assuming that each error value is independent of the others and to work with modern multi-core computers or a cluster of workstations. The numerical results show that the parallelized model order reduction algorithm is able to provide accuracy and speed up with respect to the sequential one, for both dense and sparse data sets.

关键词： computational modeling Integrated circuit modeling Mathematical model Adaptation models Program processors Accuracy Data models

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A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors

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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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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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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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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 NEW HIGH‐PRECISION, UNIVERSAL‐FREQUENCY COMPUTER COMPONENT

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Journal of the American Society for Naval Engineers 1950年第2期62卷 325-338页

作者： HERR, DONALD BLUMENSTOCK, NORMAN HONORARY MEMBER THE AUTHORS MR. HERR Honorary Member of the A.S.N.E. has the B.S. in E.E. M.S. in E.E. and E.E. degrees. He was National Coffin Foundation Fellow of the General Electric Company National Tau Beta Pi Fellow and National Sigma Tau Fellow at the Moore School of Electrical Engineering University of Pennsylvania and at M.I.T. prior to World War II. He was also awarded a National Gordon McKay Fellowship by Harvard University and received the A. Atwater Kent Award in Electrical Engineering from the University of Pennsylvania. A licensed radio amateur at 12 Mr. Herr first worked summers at RCA and Bell Laboratories and was with the General Electric Company in 1939 and 1940 as development engineer before volunteering for over five years of active Naval duty. He served as Officer-in-Charge Electrical Minesweeping Group Bureau of Ships December 1940 to April 1943 as Acting Design Superintendent and Officer-in-Charge Los Angeles-Long Beach Harbor Surge Investigation U. S. Naval Shipyard Terminal Island to November 1944 and as Research-Patents Liaison Officer Office of Naval Research to January 1946 returning to inactive duty as lieutenant commander U.S.N.R. Mr. Herr received two Navy letters of commendation. Since 1946 he was assistant to vice president in charge of the engineering division of Control Instrument Company Brooklyn New York and is project engineer at the Reeves Instrument Corporation responsible for new servo and computer component developments. Mr. Herr has been associated with Dean Harold Pender and Professor Ernst Guillemin in advanced network theory and has specialized for 12 years in development and design of servomechanisms differential analyzers computers and fire control systems utilizing advanced network analysis and synthesis methods. Mr. Herr is also presently teaching servomechanisms network-synthesis and feedback amplifier design in the Graduate School of the Polytechnic Institute of Brooklyn. He has contributed frequently to the JOURNAL OF THE AMERICA

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TWO NEW ECONOMICAL COMPUTERS FOR THE DESIGN AND ANALYSIS OF SERVOMECHANISMS, NETWORKS, AMPLIFIERS, AND ANALOGOUS DYNAMICAL systems

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Journal of the American Society for Naval Engineers 1951年第4期63卷 851-871页

作者： HERR, DONALD HONORARY MEMBER THE AUTHOR:Mr.Herr Honorary Member of the A.S.N.E. has the B.S. in E.E. M.S. in E.E. and E.E. degrees. He was National Coffin Foundation Fellow of the General Electric Company National Tau Beta Pi Fellow and National Sigma Tau Fellow at the Moore School of Electrical Engineering University of Pennsylvania and at M.I.T. prior to World War II. He was also awarded a National Gordon McKay Fellowship by Harvard University and received the A. Atwater Kent Award in Electrical Engineering from the University of Pennsylvania. A licensed radio amateur at 12 Mr. Herr first worked summers at RCA and Bell Laboratories and was with the General Electric Company in 1939 and 1940 as development engineer before volunteering for over five years of active Naval duty. He served as Officer-in-Charge Electrical Minesweeping Group Bureau of Ships December 1940 to April 1943 as Acting Design Superintendent and Officer-in-Charge Los Angeles-Long Beach Harbor Surge Investigation U. S. Naval Shipyard Terminal Island to November 1944 and as Research-Patents Liaison Officer Office of Naval Research to January 1946 returning to inactive duty as lieutenant commander U.S.N.R. Mr. Herr received two Navy letters of commendation. Since 1946 he was assistant to vice president in charge of the engineering division of Control Instrument Company Brooklyn New York and is project engineer at the Reeves Instrument Corporation responsible for new servo and computer component developments. Mr. Herr has been associated with Dean Harold Pender and Professor Ernst Guillemin in advanced network theory and has specialized for 12 years in development and design of servomechanisms differential analyzers computers and fire control systems utilizing advanced network analysis and synthesis methods. He has contributed frequently to the JournalOF THE AmericanSocietyOF NavalEngineersand was the Society's 1945 Prize Essayist on the subject: “Engineering in the Navy as seen by an Active Reserve Officer.” He is senior member of the I.R.E

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