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Volumn 30, Issue 6, 2008, Pages 3270-3288

Model reduction for large-scale systems with high-dimensional parametric input space

Author keywords

Heat conduction; Model reduction; Optimization; Sampling

Indexed keywords

ADAPTIVE ALGORITHMS; CONSTRAINED OPTIMIZATION; LARGE SCALE SYSTEMS; THERMOANALYSIS;

EID: 55149091531     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070694855     Document Type: Article
Times cited : (318)

References (32)
  • 1
    • 0013014083 scopus 로고    scopus 로고
    • Adaptive control of a wake flow using proper orthogonal decomposition
    • Shape Optimization and Optimal Design, J. Cagnol, M.P. Polis, and J.-P. Zolésio, eds, Marcel Dekker, New York
    • K. AFANASIEV AND M. HINZE, Adaptive control of a wake flow using proper orthogonal decomposition, in Shape Optimization and Optimal Design, Lecture Notes in Pure and Appl. Math. 216, J. Cagnol, M.P. Polis, and J.-P. Zolésio, eds., Marcel Dekker, New York, 2001, pp. 317-332.
    • (2001) Lecture Notes in Pure and Appl. Math , vol.216 , pp. 317-332
    • AFANASIEV, K.1    HINZE, M.2
  • 3
    • 15744385841 scopus 로고    scopus 로고
    • An "empirical interpolation" method: Application to efficient reduced-basis discretization of partial differential equations
    • M. BARRAULT, Y. MADAY, N.C. NGUYEN, AND A.T. PATERA, An "empirical interpolation" method: Application to efficient reduced-basis discretization of partial differential equations, C. R. Acad. Sci. Paris Ser. I Math., 339 (2004), pp. 339-667.
    • (2004) C. R. Acad. Sci. Paris Ser. I Math , vol.339 , pp. 339-667
    • BARRAULT, M.1    MADAY, Y.2    NGUYEN, N.C.3    PATERA, A.T.4
  • 4
    • 0032294378 scopus 로고    scopus 로고
    • Finite element methods of least squares type
    • P. BOCHEV AND M. GUNZBURGER, Finite element methods of least squares type, SIAM Rev., 40 (1998), pp. 789-837.
    • (1998) SIAM Rev , vol.40 , pp. 789-837
    • BOCHEV, P.1    GUNZBURGER, M.2
  • 6
    • 0033296256 scopus 로고    scopus 로고
    • A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems
    • M.A. BRANCH, T.F. COLEMAN, AND Y. LI, A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems, SIAM J. Sci. Comput., 21 (1999), pp. 1-23.
    • (1999) SIAM J. Sci. Comput , vol.21 , pp. 1-23
    • BRANCH, M.A.1    COLEMAN, T.F.2    LI, Y.3
  • 8
    • 0028747782 scopus 로고
    • First-order system least squares for second-order partial differential equations: Part I
    • Z. GAI, R. LAZAROV, T. MANTEUFFEL, AND S. MCCORMICK, First-order system least squares for second-order partial differential equations: Part I, SIAM J. Numer. Anal., 31 (1994), pp. 1785-1802.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 1785-1802
    • GAI, Z.1    LAZAROV, R.2    MANTEUFFEL, T.3    MCCORMICK, S.4
  • 9
    • 0000260122 scopus 로고    scopus 로고
    • Z. CAI, T. MANTEUFFEL, AND S. MCC ORMICK, First-order system least squares for second-order partial differential equations: Part II, SIAM J. Numer. Anal., 34 (1997), pp. 425-454.
    • Z. CAI, T. MANTEUFFEL, AND S. MCC ORMICK, First-order system least squares for second-order partial differential equations: Part II, SIAM J. Numer. Anal., 34 (1997), pp. 425-454.
  • 10
    • 2542503566 scopus 로고    scopus 로고
    • Multiparameter moment matching model reduction approach for generating geometrically parameterized interconnect performance models
    • L. DANIEL, O.C. SIONG, L.S. CHAY, K.H. LEE, AND J. WHITE, Multiparameter moment matching model reduction approach for generating geometrically parameterized interconnect performance models, Trans. Computer Aided Design Integrated Circuits, 23 (2004), pp. 678-693.
    • (2004) Trans. Computer Aided Design Integrated Circuits , vol.23 , pp. 678-693
    • DANIEL, L.1    SIONG, O.C.2    CHAY, L.S.3    LEE, K.H.4    WHITE, J.5
  • 11
    • 0033317391 scopus 로고    scopus 로고
    • Centroidal Voronoi tessellations: Applications and algorithms
    • Q. DU, V. FABER, AND M. GUNZBURGER, Centroidal Voronoi tessellations: Applications and algorithms, SIAM Rev., 41 (1999), pp. 637-676.
    • (1999) SIAM Rev , vol.41 , pp. 637-676
    • DU, Q.1    FABER, V.2    GUNZBURGER, M.3
  • 12
    • 0003176174 scopus 로고    scopus 로고
    • Choosing the forcing terms in an inexact Newton method
    • S.C. EISENSTAT AND H.F. WALKER, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), pp. 16-32.
    • (1996) SIAM J. Sci. Comput , vol.17 , pp. 16-32
    • EISENSTAT, S.C.1    WALKER, H.F.2
  • 15
    • 15744385753 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations, ESAIM
    • M. GREPL AND A. PATERA, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations, ESAIM Math. Modelling Numer. Anal., 39 (2005), pp. 157-181.
    • (2005) Math. Modelling Numer. Anal , vol.39 , pp. 157-181
    • GREPL, M.1    PATERA, A.2
  • 17
    • 33750482967 scopus 로고    scopus 로고
    • Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
    • M.D. GUNZBURGER, J.S. PETERSON, AND J.N. SHADID, Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data, Comput. Meth. Appl. Mech. Engrg., 196 (2007), pp. 1030-1047.
    • (2007) Comput. Meth. Appl. Mech. Engrg , vol.196 , pp. 1030-1047
    • GUNZBURGER, M.D.1    PETERSON, J.S.2    SHADID, J.N.3
  • 18
    • 55149084304 scopus 로고    scopus 로고
    • M. HINZE AND S. VOLKWEIN, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, in Dimension Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, and D. Sorensen, eds., Lecture Notes in Comput. and Appl. Math., Springer, New York, 2005, pp. 261-306.
    • M. HINZE AND S. VOLKWEIN, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, in Dimension Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, and D. Sorensen, eds., Lecture Notes in Comput. and Appl. Math., Springer, New York, 2005, pp. 261-306.
  • 20
    • 55149113391 scopus 로고    scopus 로고
    • S. KÖRKEL AND E. KOSTINA, Numerical methods for nonlinear experimental design, in Modelling, Simulation and Optimization of Complex Processes, Proceedings of the International Conference on High Performance Scientific Computing, 2003, Hanoi, Vietnam, H.G. Bock, E. Kostina, H.X. Phu, and R. Rannacher, eds., Springer, New York, 2004, pp. 255-272.
    • S. KÖRKEL AND E. KOSTINA, Numerical methods for nonlinear experimental design, in Modelling, Simulation and Optimization of Complex Processes, Proceedings of the International Conference on High Performance Scientific Computing, 2003, Hanoi, Vietnam, H.G. Bock, E. Kostina, H.X. Phu, and R. Rannacher, eds., Springer, New York, 2004, pp. 255-272.
  • 21
    • 0033177060 scopus 로고    scopus 로고
    • Control of Burgers' equation by reduced order approach using proper orthogonal decomposition
    • K. KUNISCH AND S. VOLKWEIN, Control of Burgers' equation by reduced order approach using proper orthogonal decomposition, J. Optim. Theory Appl., 102 (1999), pp. 345-371.
    • (1999) J. Optim. Theory Appl , vol.102 , pp. 345-371
    • KUNISCH, K.1    VOLKWEIN, S.2
  • 22
    • 0035176703 scopus 로고    scopus 로고
    • Modeling and control of physical processes using proper orthogonal decomposition
    • H.V. LY AND H.T. TRAN, Modeling and control of physical processes using proper orthogonal decomposition, Math. Comput. Modeling, 33 (2001), pp. 223-236.
    • (2001) Math. Comput. Modeling , vol.33 , pp. 223-236
    • LY, H.V.1    TRAN, H.T.2
  • 23
    • 77956805491 scopus 로고    scopus 로고
    • Y. MADAY, A.T. PATERA, AND D.V. ROVAS, A Blackbox Reduced-Basis Output Bound Method for Noncoercive Linear Problems, Stud. Math. Appl. 31, D. Cioranescu and J.L. Lions, eds., North-Holland, Amsterdam, 2002.
    • Y. MADAY, A.T. PATERA, AND D.V. ROVAS, A Blackbox Reduced-Basis Output Bound Method for Noncoercive Linear Problems, Stud. Math. Appl. 31, D. Cioranescu and J.L. Lions, eds., North-Holland, Amsterdam, 2002.
  • 24
    • 0018468345 scopus 로고
    • A comparison of three methods for selecting values of input variables in the analysis of output from a computer code
    • M.D. MCKAY, R.J. BECKMAN, AND W.J. CONOVER, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979), pp. 239-245.
    • (1979) Technometrics , vol.21 , pp. 239-245
    • MCKAY, M.D.1    BECKMAN, R.J.2    CONOVER, W.J.3
  • 26
    • 84855631966 scopus 로고    scopus 로고
    • Initial evaluation of pure and latinized centroidal Voronoi tessellation for non-uniform statistical sampling
    • K.M. Hanson and P.M. Hemez, eds, Los Alamos National Laboratory
    • V.J. ROMERO, J.S. BURKARDT, M.D. GUNZBURGER, AND J.S. PETERSON, Initial evaluation of pure and latinized centroidal Voronoi tessellation for non-uniform statistical sampling, in Sensitivity Analysis of Model Output, K.M. Hanson and P.M. Hemez, eds., Los Alamos National Laboratory, 2005, pp. 380-401.
    • (2005) Sensitivity Analysis of Model Output , pp. 380-401
    • ROMERO, V.J.1    BURKARDT, J.S.2    GUNZBURGER, M.D.3    PETERSON, J.S.4
  • 28
    • 33750956222 scopus 로고    scopus 로고
    • On the stability of the reduced basis method for Stokes equations in parametrized domains
    • G. ROZZA AND K. VEROY, On the stability of the reduced basis method for Stokes equations in parametrized domains, Comput. Methods Appl. Mech. Engrg., 196 (2007), pp. 1244-1260.
    • (2007) Comput. Methods Appl. Mech. Engrg , vol.196 , pp. 1244-1260
    • ROZZA, G.1    VEROY, K.2
  • 31
    • 15744406041 scopus 로고    scopus 로고
    • Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: Rigorous reduced-basis a posteriori error bounds
    • K. VEROY AND A. PATERA, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: Rigorous reduced-basis a posteriori error bounds, Internat. J. Numer. Methods Fluids, 47 (2005), pp. 773-788.
    • (2005) Internat. J. Numer. Methods Fluids , vol.47 , pp. 773-788
    • VEROY, K.1    PATERA, A.2
  • 32
    • 85088184409 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations
    • Orlando, FL
    • K. VEROY, C. PRUD'HOMME, D.V. ROVAS, AND A.T. PATERA, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, in Proceedings of the 16th AIAA Computational Fluid Dynamics Conference, Orlando, FL, 2003.
    • (2003) Proceedings of the 16th AIAA Computational Fluid Dynamics Conference
    • VEROY, K.1    PRUD'HOMME, C.2    ROVAS, D.V.3    PATERA, A.T.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.