• [1]
    A.C. Antoulas and D.C. Sorensen, Approximation of large-scale dynamical systems: An overview, Int. J. Appl. Math. Comput. Sci. 11(5), 10931121 (2001).
  • [2]
    A. Antoulas, Approximation of Large-Scale Dynamical Systems (SIAM, Philadelphia, 2005).
  • [3]
    M. Arnold and W. Schiehlen (eds.), Simulation Techniques for Applied Dynamics, CISM International Centre for Mechanical Sciences, Vol. 507 (Springer, Vienna, 2009).
  • [4]
    Z. Bai and Y. Su, Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method, SIAM J. Sci. Comput. 26, 16921709 (2005).
  • [5]
    Z. Bai and Y. Su, SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem, SIAM J. Matrix Anal. Appl. 26(3), 640659 (2005).
  • [6]
    M. Bargende, Verbrennungsmotoren 1 (in German), Vorlesungsskript (Universität Stuttgart, WS, Stuttgart, 2006).
  • [7]
    R.H. Bartels and G.W. Stewart, Solution of the matrix equation AX + XB = C [F4], Commun. ACM 15(9), 820826 (1972).
  • [8]
    P. Benner, Solving large-scale control problems, IEEE Control Syst. Mag. 14(1), 4459 (2004).
  • [9]
    P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitt. 29(2), 275296 (2006).
  • [10]
    P. Benner, P. Kürschner, and J. Saak, Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method, Numerical Algorithms, 2012, also available as preprint:
  • [11]
    P. Benner, P. Kürschner, and J. Saak, A Goal-Oriented Dual LRCF-ADI for Balanced Truncation, in: Proceedings of the MathMod 2012, preprint available at
  • [12]
    P. Benner, J.R. Li, and T. Penzl, Numerical solution of large Lyapunov equations, Riccati equations, and linear-quadratic control problems, Linear Algebr. Appl. 15(9), 755777 (2008).
  • [13]
    P. Benner and J. Saak, Efficient Balancing Based MOR for Second Order Systems Arising in Control of Machine Tools, in: Proceedings of the MathMod 2009, edited by I. Troch and F. Breitenecker, ARGESIM Reports Vol. 35 (ARGESIM, Vienna, 2009), pp. 1232–1243.
  • [14]
    P. Benner and J. Saak, Efficient balancing based MOR for large scale second order systems, Math. Comput, Model. Dyn. Syst. 17(2), 123143 (2011).
  • [15]
    Y. Chahlaoui, D. Lemonnier, A. Vandendorpe, and P.V. Dooren, Second-order balanced truncation, Linear Algebr. Appl. 415(2–3), 378384 (2006).
  • [16]
    R. Craig and M. Bampton, Coupling of substructures for dynamic analyses, AIAA J. 6(7), 13131319 (1968).
  • [17]
    R. Craig, Coupling of Substructures for Dynamic Analyses: An Overview, in: Proceedings of the AIAA Dynamics Specialists Conference, Paper-ID 2000-1573, Atlanta, USA, April 5 (AIAA, Atlanta, 2000).
  • [18]
    R. Craig and A. Kurdila, Fundamentals of Structural Dynamics, (John Wiley & Sons, New York, 2006).
  • [19]
    C. Daniel, E. Woschke, and J. Strackeljan, Integration von Tribosystemen in MKS-Modelle am Beispiel von Motorkomponenten (in German), in: Tagungsband der Magdeburger Maschinenbau-Tage (Universität Magdeburg, Magdeburg, 2007).
  • [20]
    I. Duff, A. Erisman, and J. Reid, Direct methods for sparse matrices (Oxford University Press, New York, 1986).
  • [21]
    J. Fehr, Automated and Error-controlled Model Reduction in Elastic Multibody Systems, Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 21 (Shaker Verlag, Aachen, 2011).
  • [22]
    J. Fehr and P. Eberhard, Error-controlled Model Reduction in Flexible Multibody Dynamics, J. Comput. Nonlinear Dyn. 5(3), 031005-1–031005-8 (2010).
  • [23]
    J. Fehr and P. Eberhard, Simulation Process of Flexible Multibody Systems with Non-modal Model Order Reduction Techniques, Multibody Syst. Dyn. 25(3), 313334 (2011).
  • [24]
    J. Fehr, C. Tobias, and P. Eberhard, Automated and Error-controlled Model Reduction for Durability Based Structural Optimization of Mechanical Systems, in: Proceedings of the 5th Asian Conference on Multibody Dynamics, Kyoto, Japan, August 23–26, (Kyoto University, Kyoto, 2010).
  • [25]
    K. Gallivan, A. Vandendorpe, and P. Van Dooren, Model reduction of MIMO systems via tangential interpolation, SIAM J. Matrix Anal. Appl. 26(2), 328349, (2004).
  • [26]
    W. Gawronski and J. Juang, Model reduction in limited time and frequency intervals, Int. J. Syst. Sci. 21(1), 349376, (1990).
  • [27]
    L. Grasedyck, Existence of a low rank or H-matrix approximant to the solution of a Sylvester equation, Numer. Linear Algebr. Appl. 11, 371389 (2004).
  • [28]
    E. Grimme, Krylov Projection Method for Model Reduction, Phd thesis (University of Illinois, Urbana-Champaign, 1997).
  • [29]
    S. Gugercin and A.C. Antoulas and C. Beattie, ℋ2 Model reduction for large-scale dynamical systems, SIAM J. Matrix Anal. Appl. 30(2), 609638 (2008).
  • [30]
    R.J. Guyan, Reduction of stiffness and mass matrices, AIAA J. 3(2), 380 (1965).
  • [31]
    S. Hammarling, Numerical solution of the stable, nonnegative definite Lyapunov equation, IMA J. Numer. Anal. 2(3), 303323 (1982).
  • [32]
    W.C. Hurty, Dynamic Anslysis of Structural Systems Using Component Modes. AIAA J. 3, 678685 (1965).
  • [33]
    G. Knoll, J. Lang, and R. Schönen, Strukturdynamik von Kurbelwelle und Motorblock mit elastohydrodynamischer Grundlagerkopplung (in German), in: VDI Fortschritt-Berichte, Reihe 11 Schwingungstechnik, No. 201 (VDI-Verlag and Dissertation RWTH Aachen, Aachen, 1993).
  • [34]
    G. Knoll, R. Lechtape-Güteer, R. Schönen, C. Träbing, and J. Lange, Simulationstools für strukturdynamische/elastohydrodynamisch gekoppelte Motorkomponenten (in German), FB 15, Institut für Maschinenelemente und Konstruktionstechnik (Universität GH Kassel, Kassel, Januar 2000).
  • [35]
    P. Koutsovasilis and M. Beitelschmidt, Comparison of model reduction techniques for large mechanical systems, Multibody Syst. Dyn. 20(2), 111128 (2008).
  • [36]
    P. Leger and E. Wilson, Modal summation methods for structural dynamic computations, Earthq. Eng. Struct. Dyn. 16(1), 23277 (1988).
  • [37]
    M. Lehner, Modellreduktion in elastischen Mehrkörpersystemen (in German), Dissertation, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 10 (Shaker Verlag, Aachen, 2007).
  • [38]
    M. Lehner and P. Eberhard, Modellreduktion in elastischen Mehrkörpersystemen (in German), at – Automatisierungstechnik 54, 170177 (2006).
  • [39]
    J.R. Li and J. White, Low rank solution of Lyapunov equations, SIAM J. Matrix Anal. Appl. 24(1), 260280 (2002).
  • [40]
    J. Lienemann, Complexity Reduction Techniques for Advanced MEMS Actuators Simulation, doctoral thesis, (Albert-Ludwigs-Universität, Freiburg, 2006).
  • [41]
    D.G. Meyer and S. Srinivasan, Balancing and model reduction for second-order form linear systems, IEEE Trans. Autom. Control 41(11), 16321644 (1996).
  • [42]
    B.C. Moore, Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control, 26(1), 1732, (1981).
  • [43]
    C. Nowakowski, J. Fehr, and P. Eberhard, Einfluß von Schnittstellenmodellierungen bei der Reduktion elastischer Mehrkörpersysteme (in German), at – Automatisierungstechnik 59(8), 512519 (2011).
  • [44]
    C. Nowakowski, J. Fehr, and P. Eberhard, Model reduction for a crankshaft used in coupled simulations of engines, in: Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2011, Brussels, Belgium (Louvain University, Brussels, 2011).
  • [45]
    T. Penzl, A cyclic low-rank Smith method for large sparse Lyapunov equations, SIAM J. Sci. Comput. 21(4), 14011418 (1999).
  • [46]
    T. Reis and T. Stykel, Balanced truncation model reduction of second-order systems, Math. Comput. Model. Dyn. Syst. 14(5), 391406 (2008).
  • [47]
    J. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition (SIAM, Philadelphia, 2003).
  • [48]
    J. Saak, Efficient Numerical Solution of Large Scale Algebraic Matrix Equations in PDE Control and Model Order Reduction, doctoral thesis (TU Chemnitz, Cemnitz, 2009).
  • [49]
    B. Salimbahrami and B. Lohmann, Order reduction of large scale second-order systems using Krylov subspace methods, Linear Algebr. Appl. 415(2–3), 385405 (2006).
  • [50]
    W. Schiehlen and P. Eberhard, Technische Dynamik (in German) (Vieweg+Teubner, Wiesbaden, 2012).
  • [51]
    W. Schilders, H. van der Vorst, and J. Rommes (eds.), Model Order Reduction: Theory, Research Aspects and Applications, Mathematics in Industry, Vol. 13 (Springer, Berlin, 2008).
  • [52]
    R. Schwertassek and O. Wallrapp, Dynamik flexibler Mehrkörpersysteme (in German) (Vieweg, Braunschweig, 1999).
  • [53]
    A.A. Shabana, Resonance conditions and deformable body co-ordinate systems, J. Sound Vib. 192, 389398 (1996).
  • [54]
    A.A. Shabana, Flexible multibody dynamics: Review of past and recent developments, Multibody Syst. Dyn. 1(2), 159223 (1997).
  • [55]
    V. Simoncini, A new iterative method for solving large-scale Lyapunov matrix equations, SIAM J. Sci. Comput., 29(3), 12681288 (2007).
  • [56]
    D. Sorensen and Y. Zhou, Bounds on eigenvalue decay rates and sensitivity of solutions to Lyapunov equations, Tech. rep. tr02-07 (Dept. of Computational and Applied Mathematics, Houston, Hune 2002).
  • [57]
    F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43(2), 235286 (2001).
  • [58]
    R. van Basshuysen and F. Schäfer (eds.), Lexikon Motorentechnik, Der Verbrennungsmotor von A–Z (in German) (Vieweg, Wiesbaden, April 2004).
  • [59]
    R. van Basshysen and F. Schäfer (eds.), Handbuch Verbrennungsmotor, Grundlagen, Komponenten, Systeme, Perspektiven (in German) (Vieweg Teubner, Wiesbaden, 2010).
  • [60]
    E. Wachspress, Iterative solution of the Lyapunov matrix equation, Appl. Math. Lett. 107, 8790 (1988).
  • [61]
    E. Wachspress, The ADI Model Problem (E.L. Wachspress, Windsor, CA, 1995)
  • [62]
    K. Willner, Methode der finiten Elemente (in German) Vorlesungsskript (Universität Stuttgart, Institut A für Mechanik, 1999).
  • [63]
    B. Yan, S.X.D. Tan, and B. McGaughy, Second-order balanced truncation for passive-order reduction of RLCK circuits, IEEE Trans. Circuit Syst. II 55(9), 942946 (2008).
  • [64]
    S. Zima, Kurbeltriebe: Konstruktion, Berechnung und Erprobung von den Anfängen bis heute (in German) (Vieweg, Wiesbaden, 1999).