Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. C. Antoulas, D. C. Sorensen, and S. Gugercin. A survey of model reduction methods for large-scale systems. Structured Matrices in Operator Theory, Numerical Analysis, Control, Signal and Image Processing. Contemporary Mathematics. AMS publications, 2001.
Z. Bai. Krylov subspace techniques for reduced-order modeling of large scale dynamical systems. Applied Numerical Mathematics, 43:9–44, 2002.
M. J. Balas. Trends in large space structure control theory: fondest theory, wildest dreams. IEEE Trans. Automat. Control, AC-27:522–535, 1982.
Z. Bai, D. Bindel, J. Clark, J. Demmel, K. S. J. Pister, and N. Zhou. New numerical techniques and tools in SUGAR for 3D MEMS simulation. In Technical Proceedings of the Fourth International Conference on Modeling and Simulation of Microsystems, pages 31–34, 2000.
Z. Bai and Y. Su. Dimension reduction of second-order dynamical systems via a second-order Arnoldi method. SIAM J. Sci. Comp., 2004. to appear.
Z. Bai and Y. Su. SOAR: A second-order arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. Appl., 2004. to appear.
Y. Chahlaoui, D. Lemonnier, K. Meerbergen, A. Vandendorpe, and P. Van Dooren. Model reduction of second order systems. In Proceedings of 15th International Symposium on Mathematical Theory of Networks and Systems, University of Notre Dame, 2002.
R. R. Craig, Jr. Structural Dynamics: An Introduction to Computer Methods. John Wiley & Sons, 1981.
J. V. Clark, N. Zhou, D. Bindel, L. Schenato, W. Wu, J. Demmel, and K. S. J. Pister. 3D MEMS simulation using modified nodal analysis. In Proceedings of Microscale Systems: Mechanics and Measurements Symposium, pages 68–75, 2000.
J. V. Clark, N. Zhou, and K. S. J. Pister. MEMS simulation using SUGAR v0.5. In Proc. Solid-State Sensors and Actuators Workshop, Hilton Head Island, SC, pages 191–196, 1998.
R. W. Freund. Krylov-subspace methods for reduced-order modeling in circuit simulation. J. Comput. Appl. Math., 123:395–421, 2000.
Free Field Technologies. MSC.Actran 2003, User's Manual, 2003.
S. D. Garvey, Z. Chen, M. I. Friswell, and U. Prells. Model reduction using structure-preserving transformations. In Proceedings of the International Modal Analysis Conference IMAC XXI, pages 361–377. Kissimmee, Florida, Feb., 2003.
K. Meerbergen. The solution of parametrized symmetric linear systems. SIAM J. Matrix Anal. Appl., 24(4):1038–1059, 2003.
K. Meerbergen and M. Robbé. The Arnoldi method for the solution of the quadratic eigenvalue problem and parametrized equations, 2003. Submitted for publication.
D. G. Meyer and S. Srinivasan. Balancing and model reduction for second-order form linear systems. IEEE Trans. Automatic Control, 41:1632–1644, 1996.
V. Mehrmann and D. Watkins. Structure-preserving methods for computing eigenpairs of large sparse skew-hamiltonian/hamiltonian pencils. SIAM J. Matrix Anal. Applic., 22(6):1905–1925, 2001.
A. Odabasioglu, M. Celik, and L.T. Pileggi. PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, 17:645–654, 1998.
P. M. Pinsky and N. N. Abboud. Finite element solution of the transient exterior structural acoustics problem based on the use of radially asymptotic boundary conditions. Computer Methods in Applied Mechanics and Engineering, 85:311–348, 1991.
D. Ramaswamy and J. White. Automatic generation of small-signal dynamic macromodels from 3-D simulation. In Technical Proceedings of the Fourth International Conference on Modeling and Simulation of Microsystems, pages 27–30, 2000.
T.-J. Su and R. R. Craig Jr. Model reduction and control of flexible structures using Krylov vectors. J. of Guidance, Control and Dynamics, 14:260–267, 1991.
B. Salimbahrami and B. Lohmann. Order reduction of large scale second order systems using Krylov subspace methods. Lin. Alg. Appl., 2004. to appear.
R. D. Slone. Fast frequency sweep model order reduction of polynomial matrix equations resulting from finite element discretization. PhD thesis, Ohio State University, Columbus, OH, 2002.
G. W. Stewart. Matrix Algorithms, Vol II: Eigensystems. SIAM, Philadelphia, 2001.
F. Tisseur and K. Meerbergen. The quadratic eigenvalue problem. SIAM Rev., 43(2):235–286, 2001.
T. Wittig, I. Munteanu, R. Schuhmann, and T. Weiland. Two-step Lanczos algorithm for model order reduction. IEEE Trans. Magn., 38:673–676, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bai, Z., Meerbergen, K., Su, Y. (2005). Arnoldi Methods for Structure-Preserving Dimension Reduction of Second-Order Dynamical Systems. In: Benner, P., Sorensen, D.C., Mehrmann, V. (eds) Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27909-1_7
Download citation
DOI: https://doi.org/10.1007/3-540-27909-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24545-2
Online ISBN: 978-3-540-27909-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)