메뉴 건너뛰기




Volumn 415, Issue 2-3, 2006, Pages 262-289

Balanced truncation model reduction for semidiscretized Stokes equation

Author keywords

Balanced truncation; Controllability and observability Gramians; Descriptor system; Hankel singular values; Model reduction; Projected generalized Lyapunov equation; Stokes equation

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONTROLLABILITY; LYAPUNOV METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING;

EID: 33646489022     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2004.01.015     Document Type: Article
Times cited : (63)

References (40)
  • 1
    • 0010011201 scopus 로고    scopus 로고
    • A survey of model reduction methods for large-scale systems
    • Structured Matrices in Mathematics, Computer Science and Engineering. Olshevsky V. (Ed), American Mathematical Society
    • Antoulas A.C., Sorensen D.C., and Gugercin S. A survey of model reduction methods for large-scale systems. In: Olshevsky V. (Ed). Structured Matrices in Mathematics, Computer Science and Engineering. Contemporary Mathematics Series, 280 vol. I (2001), American Mathematical Society
    • (2001) Contemporary Mathematics Series, 280 , vol.I
    • Antoulas, A.C.1    Sorensen, D.C.2    Gugercin, S.3
  • 2
    • 0037103431 scopus 로고    scopus 로고
    • On the decay rate of the Hankel singular values and related issues
    • Antoulas A.C., Sorensen D.C., and Zhou Y. On the decay rate of the Hankel singular values and related issues. Systems Control Lett. 46 5 (2002) 323-342
    • (2002) Systems Control Lett. , vol.46 , Issue.5 , pp. 323-342
    • Antoulas, A.C.1    Sorensen, D.C.2    Zhou, Y.3
  • 3
    • 0023328005 scopus 로고
    • Lyapunov-like equations and reachability/observability Gramians for descriptor systems
    • Bender D.J. Lyapunov-like equations and reachability/observability Gramians for descriptor systems. IEEE Trans. Automat. Control 32 4 (1987) 343-348
    • (1987) IEEE Trans. Automat. Control , vol.32 , Issue.4 , pp. 343-348
    • Bender, D.J.1
  • 4
    • 0034825391 scopus 로고    scopus 로고
    • Flow control: new challenges for a new Renaissance
    • Bewley T.R. Flow control: new challenges for a new Renaissance. Prog. Aerospace Sci. 37 (2001) 21-58
    • (2001) Prog. Aerospace Sci. , vol.37 , pp. 21-58
    • Bewley, T.R.1
  • 6
    • 0027608731 scopus 로고
    • The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applications. Part I: Theory and algorithms
    • Demmel J.W., and Kå B. The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applications. Part I: Theory and algorithms. ACM Trans. Math. Software 19 2 (1993) 160-174
    • (1993) ACM Trans. Math. Software , vol.19 , Issue.2 , pp. 160-174
    • Demmel, J.W.1    Kå, B.2
  • 9
    • 0029308198 scopus 로고
    • Efficient linear circuit analysis by Padé approximation via the Lanzcos process
    • Feldmann P., and Freund R.W. Efficient linear circuit analysis by Padé approximation via the Lanzcos process. IEEE Trans. Comput.-Aided Des. 14 (1995) 639-649
    • (1995) IEEE Trans. Comput.-Aided Des. , vol.14 , pp. 639-649
    • Feldmann, P.1    Freund, R.W.2
  • 11
    • 0034322885 scopus 로고    scopus 로고
    • Krylov-subspace methods for reduced-order modeling in circuit simulation
    • Freund R.W. Krylov-subspace methods for reduced-order modeling in circuit simulation. J. Comput. Appl. Math. 123 1-2 (2000) 395-421
    • (2000) J. Comput. Appl. Math. , vol.123 , Issue.1-2 , pp. 395-421
    • Freund, R.W.1
  • 12
    • 0001536567 scopus 로고
    • Asymptotic waveform evaluation via a Lanczos method
    • Gallivan K., Grimme E., and Van Dooren P. Asymptotic waveform evaluation via a Lanczos method. Appl. Math. Lett. 7 (1994) 75-80
    • (1994) Appl. Math. Lett. , vol.7 , pp. 75-80
    • Gallivan, K.1    Grimme, E.2    Van Dooren, P.3
  • 13
    • 21344460034 scopus 로고    scopus 로고
    • A rational Lanczos algorithm for model reduction
    • Gallivan K., Grimme E., and Van Dooren P. A rational Lanczos algorithm for model reduction. Numer. Algorithms 12 1-2 (1996) 33-63
    • (1996) Numer. Algorithms , vol.12 , Issue.1-2 , pp. 33-63
    • Gallivan, K.1    Grimme, E.2    Van Dooren, P.3
  • 14
    • 0021441691 scopus 로고
    • ∞-errors bounds
    • ∞-errors bounds. Internat. J. Control 39 6 (1984) 1115-1193
    • (1984) Internat. J. Control , vol.39 , Issue.6 , pp. 1115-1193
    • Glover, K.1
  • 15
    • 27544508073 scopus 로고    scopus 로고
    • Model reduction of state space systems via an implicitly restarted Lanczos method
    • Grimme E.J., Sorensen D.C., and Van Dooren P. Model reduction of state space systems via an implicitly restarted Lanczos method. Numer. Algorithms 12 1-2 (1996) 1-31
    • (1996) Numer. Algorithms , vol.12 , Issue.1-2 , pp. 1-31
    • Grimme, E.J.1    Sorensen, D.C.2    Van Dooren, P.3
  • 17
    • 0023288081 scopus 로고
    • Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
    • Laub A.J., Heath M.T., Paige C.C., and Ward R.C. Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Trans. Automat. Control, AC 32 2 (1987) 115-122
    • (1987) IEEE Trans. Automat. Control, AC , vol.32 , Issue.2 , pp. 115-122
    • Laub, A.J.1    Heath, M.T.2    Paige, C.C.3    Ward, R.C.4
  • 18
    • 33646466588 scopus 로고    scopus 로고
    • J.-R. Li, Model reduction of large linear systems via low rank system Gramians, Ph.D. Thesis, Department of Mathematics, Massachusetts Institute of Technology, 2000.
  • 21
    • 0024750490 scopus 로고
    • Singular perturbation approximation of balanced systems
    • Liu Y., and Anderson B.D.O. Singular perturbation approximation of balanced systems. Internat. J. Control 50 (1989) 1379-1405
    • (1989) Internat. J. Control , vol.50 , pp. 1379-1405
    • Liu, Y.1    Anderson, B.D.O.2
  • 22
    • 0040201321 scopus 로고    scopus 로고
    • Canonical projectors for linear differential algebraic equations
    • März R. Canonical projectors for linear differential algebraic equations. Comput. Math. Appl. 31 4-5 (1996) 121-135
    • (1996) Comput. Math. Appl. , vol.31 , Issue.4-5 , pp. 121-135
    • März, R.1
  • 23
    • 0019533482 scopus 로고
    • Principal component analysis in linear systems: controllability, observability, and model reduction
    • Moore B.C. Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Automat. Control, AC 26 1 (1981) 17-32
    • (1981) IEEE Trans. Automat. Control, AC , vol.26 , Issue.1 , pp. 17-32
    • Moore, B.C.1
  • 25
    • 0033295674 scopus 로고    scopus 로고
    • A cyclic low-rank Smith method for large sparse Lyapunov equations
    • Penzl T. A cyclic low-rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. Comput. 21 4 (1999/2000) 1401-1418
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.4 , pp. 1401-1418
    • Penzl, T.1
  • 26
    • 0001082478 scopus 로고    scopus 로고
    • Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
    • Penzl T. Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case. Syst. Control Lett. 40 2 (2000) 139-144
    • (2000) Syst. Control Lett. , vol.40 , Issue.2 , pp. 139-144
    • Penzl, T.1
  • 27
    • 33646471189 scopus 로고    scopus 로고
    • T. Penzl, LYAPACK Users Guide, Preprint SFB393/00-33, Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany, August 2000. Available from .
  • 28
    • 33646466262 scopus 로고    scopus 로고
    • T. Penzl, Algorithms for model reduction of large dynamical systems. Preprint SFB 393/99-40, Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany, December 1999. Available from .
  • 29
    • 0034327551 scopus 로고    scopus 로고
    • A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
    • Ravindran S.S. A reduced-order approach for optimal control of fluids using proper orthogonal decomposition. Internat. J. Numer. Methods Fluids 34 5 (2000) 425-448
    • (2000) Internat. J. Numer. Methods Fluids , vol.34 , Issue.5 , pp. 425-448
    • Ravindran, S.S.1
  • 31
    • 0024700032 scopus 로고
    • A Schur method for balanced-truncation model reduction
    • Safonov M.G., and Chiang R.Y. A Schur method for balanced-truncation model reduction. IEEE Trans. Automat. Control, AC 34 7 (1989) 729-733
    • (1989) IEEE Trans. Automat. Control, AC , vol.34 , Issue.7 , pp. 729-733
    • Safonov, M.G.1    Chiang, R.Y.2
  • 32
    • 33646482823 scopus 로고    scopus 로고
    • D.C. Sorensen, Y. Zhou, Bounds on eigenvalue decay rates and sensitivity of solutions of Lyapunov equations, Technical Report TR02-07, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 2002.
  • 34
    • 33646493272 scopus 로고    scopus 로고
    • T. Stykel, Analysis and numerical solution of generalized Lyapunov equations, Ph.D. Thesis, Institut für Mathematik, Technische Universität Berlin, Berlin, 2002.
  • 35
    • 2342512219 scopus 로고    scopus 로고
    • T. Stykel, Gramian based model reduction for descriptor systems, Math. Control Signals Systems, 2004, to appear.
  • 36
    • 0023439931 scopus 로고
    • Truncated balanced realization of a stable non-minimal state-space system
    • Tombs M.S., and Postlethweite I. Truncated balanced realization of a stable non-minimal state-space system. Internat. J. Control 46 4 (1987) 1319-1330
    • (1987) Internat. J. Control , vol.46 , Issue.4 , pp. 1319-1330
    • Tombs, M.S.1    Postlethweite, I.2
  • 37
    • 33646469815 scopus 로고    scopus 로고
    • A. Varga, Efficient minimal realization procedure based on balancing, in: A. EL Moudni, P. Borne, S.G. Tzafestas (Eds.), Proceedings of IMACS/IFAC Symposium on Modelling and Control of Technological Systems, Lille, France, May 7-10, 1991, vol. 2, 1991, pp. 42-47.
  • 38
    • 33646487982 scopus 로고    scopus 로고
    • S. Volkwein, Optimal and suboptimal control of partial differential equations: augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition, Grazer Mathematische Berichte, 343, Karl-Franzens-Universität Graz, Graz, 2001.
  • 40
    • 33646489256 scopus 로고    scopus 로고
    • J. Weickert, Applications of the theory of differential-algebraic equations to partial differential equations of fluid dynamics, Ph.D. Thesis, Technische Universität Chemnitz, Chemnitz, 1997.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.