메뉴 건너뛰기




Volumn 13, Issue 6, 2010, Pages 249-264

Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables

Author keywords

Domain decomposition; Model reduction; Optimal control; Shape optimization

Indexed keywords

BALANCED TRUNCATION; DIMENSION REDUCTION; DOMAIN DECOMPOSITIONS; LINEAR TIME; MODEL REDUCTION; NUMERICAL SOLUTION OF PDE; OPTIMAL CONTROL; OPTIMAL CONTROL PROBLEM; OPTIMALITY; OPTIMALITY SYSTEM; OPTIMIZATION PROBLEMS; OPTIMIZATION VARIABLES; PDE-CONSTRAINED OPTIMIZATION; SHAPE OPTIMIZATION PROBLEM;

EID: 79953779816     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-010-0142-4     Document Type: Article
Times cited : (44)

References (26)
  • 1
    • 0345352838 scopus 로고    scopus 로고
    • A variational finite element method for source inversion for convective-diffusive transport
    • Akçelik, V., Biros, G., Ghattas, O., Long, K.R., van Bloemen Waanders, B.: A variational finite element method for source inversion for convective-diffusive transport. Finite Elem. Anal. Des. 39(8), 683-705 (2003)
    • (2003) Finite Elem. Anal. Des. , vol.39 , Issue.8 , pp. 683-705
    • Akçelik, V.1    Biros, G.2    Ghattas, O.3    Long, K.R.4    Van Bloemen Waanders, B.5
  • 5
    • 26844470109 scopus 로고    scopus 로고
    • Optimal control and numerical adaptivity for advection-diffusion equations
    • DOI 10.1051/m2an:2005044
    • Dedé, L., Quarteroni, A.: Optimal control and numerical adaptivity for advection-diffusion equations. ESAIM: Math. Model. Numer. Anal. 39, 1019-1040 (2005) (Pubitemid 41452244)
    • (2005) Mathematical Modelling and Numerical Analysis , vol.39 , Issue.5 , pp. 1019-1040
    • Dede, L.1    Quarteroni, A.2
  • 8
    • 0035632634 scopus 로고    scopus 로고
    • Multimodels for incompressible flows: Iterative solutions for the Navier-Stokes/Oseen coupling
    • Fatone, L., Gervasio, P., Quarteroni, A.: Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling. M2AN Math. Model. Numer. Anal. 35(3), 549-574 (2001)
    • (2001) M2AN Math. Model. Numer. Anal. , vol.35 , Issue.3 , pp. 549-574
    • Fatone, L.1    Gervasio, P.2    Quarteroni, A.3
  • 9
    • 0035824658 scopus 로고    scopus 로고
    • On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels
    • DOI 10.1016/S0045-7825(01)00302-4, PII S0045782501003024, Minisymposium on Methods for Flow Simulation and Modeling
    • Formaggia, L., Gerbeau, J.F., Nobile, F., Quarteroni, A.: On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191 (6-7), 561-582 (2001) (Pubitemid 34004491)
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.191 , Issue.6-7 , pp. 561-582
    • Formaggia, L.1    Gerbeau, J.F.2    Nobile, F.3    Quarteroni, A.4
  • 10
    • 0021441691 scopus 로고
    • All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds
    • Glover, K.: All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds. Int. J. Control 39(6), 1115-1193 (1984) (Pubitemid 14606446)
    • (1984) International Journal of Control , vol.39 , Issue.6 , pp. 1115-1193
    • Glover Keith1
  • 11
    • 0007247902 scopus 로고    scopus 로고
    • 2nd edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Principles and techniques of algorithmic differentiation
    • Griewank, A., Walther, A.: Evaluating Derivatives, 2nd edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2008). Principles and techniques of algorithmic differentiation
    • (2008) Evaluating Derivatives
    • Griewank, A.1    Walther, A.2
  • 12
    • 0037276767 scopus 로고    scopus 로고
    • A modified lowrank Smith method for large-scale Lyapunov equations
    • Gugercin, S., Sorensen, D.C., Antoulas, A.C.: A modified lowrank Smith method for large-scale Lyapunov equations. Numer. Algorithms 32(1), 27-55 (2003)
    • (2003) Numer. Algorithms , vol.32 , Issue.1 , pp. 27-55
    • Gugercin, S.1    Sorensen, D.C.2    Antoulas, A.C.3
  • 14
    • 33750977082 scopus 로고    scopus 로고
    • Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control
    • Benner, P., Mehrmann, V., Sorensen, D.C. (eds.), Springer, Heidelberg
    • Hinze, M., Volkwein, S.: Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control. In: Benner, P., Mehrmann, V., Sorensen, D.C. (eds.) Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol. 45, pp. 261-306. Springer, Heidelberg (2005)
    • (2005) Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering , vol.45 , pp. 261-306
    • Hinze, M.1    Volkwein, S.2
  • 16
    • 0036566376 scopus 로고    scopus 로고
    • A subspace approach to balanced truncation for model reduction of nonlinear control systems
    • DOI 10.1002/rnc.657
    • Lall, S., Marsden, J.E., Glavaški, S.: A subspace approach to balanced truncation for model reduction of nonlinear control systems. Int. J. Robust Nonlinear Control 12(6), 519-535 (2002) (Pubitemid 34520056)
    • (2002) International Journal of Robust and Nonlinear Control , vol.12 , Issue.6 , pp. 519-535
    • Lall, S.1    Marsden, J.E.2    Glavaski, S.3
  • 17
    • 1342283898 scopus 로고    scopus 로고
    • Reduced-order modeling: New approaches for computational physics
    • Lucia, D.J., Beran, P.S., Silva, W.A.: Reduced-order modeling: new approaches for computational physics. Prog. Aerosp. Sci. 40 (1-2), 51-117 (2004)
    • (2004) Prog. Aerosp. Sci. , vol.40 , Issue.1-2 , pp. 51-117
    • Lucia, D.J.1    Beran, P.S.2    Silva, W.A.3
  • 18
    • 0036848254 scopus 로고    scopus 로고
    • Domain decomposition for reduced-order modeling of a flow with moving shocks
    • Lucia, D.J., King, P.I., Beran, P.S.: Domain decomposition for reduced-order modeling of a flow with moving shocks. AIAA J. 40, 2360-2362 (2002) (Pubitemid 35361060)
    • (2002) AIAA Journal , vol.40 , Issue.11 , pp. 2360-2362
    • Lucia, D.J.1    King, P.I.2    Beran, P.S.3
  • 19
    • 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 26(1), 17-32 (1981)
    • (1981) IEEE Trans. Automat. Control , vol.26 , Issue.1 , pp. 17-32
    • Moore, B.C.1
  • 20
    • 84902343352 scopus 로고    scopus 로고
    • Computational vascular fluid dynamics: Problems, models and methods
    • Quarteroni, A., Tuveri, M., Veneziani, A.: Computational vascular fluid dynamics: problems, models and methods. Comput. Vis. Sci. 2(4), 163-197 (2000)
    • (2000) Comput. Vis. Sci. , vol.2 , Issue.4 , pp. 163-197
    • Quarteroni, A.1    Tuveri, M.2    Veneziani, A.3
  • 21
    • 0002342184 scopus 로고    scopus 로고
    • INTLAB-INTerval LABoratory
    • Csendes, T. (ed.), Kluwer, Dordrecht
    • Rump, S.M.: INTLAB-INTerval LABoratory. In: Csendes, T. (ed.) Developments in Reliable Computing, pp. 77-104. Kluwer, Dordrecht (1999). http://www.ti3.tu-harburg.de/rump/
    • (1999) Developments in Reliable Computing , pp. 77-104
    • Rump, S.M.1
  • 24
    • 79953794691 scopus 로고    scopus 로고
    • Domain decomposition and model reduction of systems with local nonlinearities
    • Kunisch, K., Of, G., Steinbach, O. (eds.), Springer, Heidelberg
    • Sun, K., Glowinski, R., Heinkenschloss, M., Sorensen, D.C. : Domain decomposition and model reduction of systems with local nonlinearities. In: Kunisch, K., Of, G., Steinbach, O. (eds.) Numerical Mathematics and Advanced Applications. ENUMATH 2007., pp. 389-396. Springer, Heidelberg (2008)
    • (2008) Numerical Mathematics and Advanced Applications. ENUMATH 2007 , pp. 389-396
    • Sun, K.1    Glowinski, R.2    Heinkenschloss, M.3    Sorensen, D.C.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.