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International Conference on Computer and Information Technology

作者： Peter Benner Jens Saak M. Monir Uddin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstra?e 1 D-39106 Magdeburg Germany Department of Mathematics and Physics North South University 15/B Bashundhara Dhaka-1239 Bangladesh

ISBN: (纸本)9781509040919

Large sparse second order index-1 descriptor systems arise in various disciplines of science and engineering, such as constraint mechanics or multibody dynamics, mechatronics (where mechanical and electrical elements are coupled), but also RLC circuit design. Simulation, controller design and design optimization are only some applications of such models. Either of these tasks, just like any other many-query situation becomes unfeasible when the system is high dimensional. This paper discusses an algorithm to obtain a reduced state space model of a large sparse second order index-1 system using an interpolatory projection method based on the iterative rational Krylov algorithm (IRKA). In each iteration of this algorithm, we need to solve a number of linear systems. The main contribution of this paper is to solve these linear systems by exploiting the sparsity of the original model, which reduces the computational cost drastically. The algorithm is applied to a micro-mechanical piezo-actuated structural FEM model of a certain building block of a machine tool. Numerical experiments with a complex 3d model of an adaptive spindle support (a piezo-mechanical multiphysics system) show the effectivity and efficiency of the techniques.

关键词： second order index-1 systems sparsity model reduction interpolatory projections

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Adjoint-Based Optimal Boundary control of a Stefan Problem System Fully Coupled with Navier-Stokes Equations

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PAMM 2016年第1期16卷

作者： Björn Baran Jan Heiland Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg

Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of these problems appear even more interesting since certain desired shapes of the boundaries improve, e.g., the material quality in the case of crystal growth. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. In the work presented, we take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state at a final time as well as the control costs. Following the “optimize-then-discretize” paradigm, we formulate a first order optimality system using the formal Lagrange approach and derive the adjoint PDE system that provides the needed gradient of the cost functional. By means of an example setup of a container with an in- and outflow of water and a cooling unit at the bottom, we illustrate how the derived formulations can be used to achieve a desired interface between the solid and the fluid phase by controlling the flow at the inlet. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Numerical solution to low rank perturbed Lyapunov equations by the sign function method

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PAMM 2016年第1期16卷

作者： Peter Benner Jonas Denißen Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Germany

We investigate the numerical solution to a low rank perturbed Lyapunov equation A T X + XA = W via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], but here we focus on a framework where the matrix A has a special structure, i. e. A = B + UCV T , where B is a blockdiagonal matrix and UCV T is a low rank perturbation. We show that this structure can be kept throughout the sign function iteration but the rank of the perturbation doubles per iteration. Therefore, we apply a low rank approximation to the perturbation in order to keep its numerical rank small. We compare the standard SFM with its structure preserving variant presented in this paper by means of numerical examples from viscously damped mechanical systems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Solving Differential Matrix Equations using Parareal

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PAMM 2016年第1期16卷

作者： Martin Köhler Norman Lang Jens Saak Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Computational Methods in Systems and Control Theory Technische Universität Chemnitz Faculty of Mathematics

Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems and many more. Here, we will focus on differential Riccati equations (DRE). Solving such matrix-valued ordinary differential equations (ODE) is a highly time consuming process. We present a Parareal based algorithm applied to Rosenbrock methods for the solution of the matrix-valued differential Riccati equations. Considering problems of moderate size, direct matrix equation solvers for the solution of the algebraic Lyapunov equations arising inside the time intgration methods are used. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Distributed optimal control problems governed by coupled convection dominated PDEs with control constraints

Lecture Notes in Computational Science and Engineering

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Lecture Notes in computational Science and Engineering 2015年 103卷 469-478页

作者： Yücel, Hamdullah Benner, Peter Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches. © Springer International Publishing Switzerland 2015.

关键词： Optimal control systems

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26th Annual computational Neuroscience Meeting (CNS*2017) of the Organization for computational Neuroscience Antwerp, Belgium, July 15-20, 2017

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BMC NEUROSCIENCE 2017年第SUPPL 1期18卷 59-59页

作者： [Anonymous] Indiana University Purdue University Indianapolis Indianapolis IN 46032 USA Stark Neurosciences Research Institute Indiana University School of Medicine Indianapolis IN 46032 USA Department of Mathematics East Carolina University Greenville NC 27858 USA Jülich Supercomputing Centre Forschungszentrum Jülich 52425 Jülich Germany Future Systems Swiss National Supercomputing Centre 8092 Zurich Switzerland User Engagement and Support Swiss National Supercomputing Centre 6900 Lugano Switzerland Institut de Neurosciences des Systèmes Aix Marseille Univ 13005 Marseille France Simulation Lab Neuroscience Forschungszentrum Jülich Jülich Germany Department of Experimental Psychology Ghent University 9000 Ghent Belgium Donders Center for Cognitive Neuroimaging Radboud University 6525HR Nijmegen The Netherlands Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309 USA Department of Neurosurgery Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Neurology Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Otolaryngology Johns Hopkins School of Medicine Baltimore MD 21287 USA INSERM U968 Paris France Sorbonne Universités UPMC University Paris 06 UMR_S 968 Institut de la Vision Paris France CNRS UMR_7210 Paris France Department of Computer Architecture and Technology University of Granada (CITIC) Granada Spain Sorbonne Universités UPMC Univ Paris 06 INSERM CNRS Institut de la Vision Paris France Department of Adaptive Machine Systems Osaka University Osaka Japan Department of Computer Science University of Cergy-Pontoise Cergy-Pontoise France Department of Physics and Astronomy College of Charleston Charleston SC 29424 USA School of Physics Faculty of Science University of Sydney Sydney NSW 2006 Australia Center of Excellence for Integrative Brain Function Australian Research Council Sydney Australia Max Planck Institute for Human Cognitive and Brain Sciences Saxony Lei

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Variational Analysis of the Spectral Abscissa at a Matrix with a Nongeneric Multiple Eigenvalue

Set-Valued and Variational Analysis

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Set-Valued and Variational Analysis 2014年第1期22卷 19-43页

作者： Grundel, Sara Overton, Michael L. Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Madgeburg Germany Courant Institute of Mathematical Sciences New York University 251 Mercer Street NY NY 10012 United States

The spectral abscissa is a fundamental map from the set of complex matrices to the real numbers. Denoted α and defined as the maximum of the real parts of the eigenvalues of a matrix X, it has many applications in stability analysis of dynamical systems. The function α is nonconvex and is non-Lipschitz near matrices with multiple eigenvalues. Variational analysis of this function was presented in Burke and Overton (Math Program 90:317-352, 2001), including a complete characterization of its regular subgradients and necessary conditions which must be satisfied by all its subgradients. A complete characterization of all subgradients of α at a matrix X was also given for the case that all active eigenvalues of X (those whose real part equals α(X)) are nonderogatory (their geometric multiplicity is one) and also for the case that they are all nondefective (their geometric multiplicity equals their algebraic multiplicity). However, necessary and sufficient conditions for all subgradients in all cases remain unknown. In this paper we present necessary and sufficient conditions for the simplest example of a matrix X with a derogatory, defective multiple eigenvalue. © 2013 Springer Science+Business Media Dordrecht.

关键词： Matrix algebra

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A Cache-Aware Implementation of the Spectral Divide-and-Conquer Approach for the Non-Symmetric Generalized Eigenvalue Problem

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PAMM 2014年第1期14卷

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

We propose a new implementation of the sign function based spectral divide-and-conquer method for the generalized non-symmetric eigenvalue problem. The basic idea is to use the generalized matrix sign function to split the spectrum and the corresponding deflating subspaces and to build a recursive scheme on top of this. The method focuses on an extensive usage of scalable level 3 BLAS operations in order to achieve a good performance on modern computer architectures which makes it computationally superior to current implementations of the classical QZ algorithm. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Spectral Bounds on the Solution of Linear Time-Periodic systems

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PAMM 2014年第1期14卷

作者： Peter Benner Jonas Denißen Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Germany

Linear time-periodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Stability of the solution may be proven by rigorous bounds on the solution. The key idea of this paper is to derive Chebyshev projection bounds on the original system by solving an approximated system. Depending on the smoothness of the original function, we formulate two upper bounds. The theoretical results are illustrated and compared to trigonometric spline bounds by means of two examples which include an anisotropic rotor-bearing system. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Numerical Solution of Large Scale Sparse Matrix Equations in Python

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PAMM 2014年第1期14卷

作者： Björn Baran Martin Köhler Nitin Prasad Jens Saak Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg Department of Electrical Engineering Indian Institute of Technology Madras Chennai - 600036.

The M.E.S.S. software suite for solving large scale matrix equations and related problems is the successor of the obsolete LyaPack MATLAB® toolbox. The software suite consists of a new MATLAB toolbox and a separate C library C-M.E.S.S. which works independent from MATLAB. Due to the fact that many scientists use Python with NumPy and SciPy for their computations, we want to provide the key algorithms of M.E.S.S. there as well. In this paper, we describe and compare two possible approaches for the implementation, with special focus on their multicore performance. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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