메뉴 건너뛰기




Volumn 200, Issue 13-16, 2011, Pages 1455-1466

A high-performance parallel implementation of the certified reduced basis method

Author keywords

A posteriori error bounds; Boussinesq equation; Finite element methods; High performance computing; Reduced basis method; Sensitivity derivatives

Indexed keywords

BOUSSINESQ EQUATIONS; HIGH-PERFORMANCE COMPUTING; POSTERIORI ERROR; REDUCED BASIS METHODS; SENSITIVITY DERIVATIVES;

EID: 78951483251     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.12.026     Document Type: Article
Times cited : (42)

References (33)
  • 1
    • 0036776433 scopus 로고    scopus 로고
    • Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
    • Bai Z.J. Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 2002, 43(1-2):9-44.
    • (2002) Appl. Numer. Math. , vol.43 , Issue.1-2 , pp. 9-44
    • Bai, Z.J.1
  • 2
    • 0035000048 scopus 로고    scopus 로고
    • Model-order reduction of nonlinear MEMS devices through arclength-based Karhunen-Loéve decomposition, in: Proceeding of the IEEE international Symposium on Circuits and Systems
    • J. Chen, S.-M. Kang, Model-order reduction of nonlinear MEMS devices through arclength-based Karhunen-Loéve decomposition, in: Proceeding of the IEEE international Symposium on Circuits and Systems, vol. 2, 2001, pp. 457-460.
    • (2001) , vol.2 , pp. 457-460
    • Chen, J.1    Kang, S.-M.2
  • 3
    • 33750482967 scopus 로고    scopus 로고
    • Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
    • Gunzburger M.D., Peterson J., Shadid J.N. Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data. Comput. Meth. Appl. Mech. Engrg. 2007, 196:1030-1047.
    • (2007) Comput. Meth. Appl. Mech. Engrg. , vol.196 , pp. 1030-1047
    • Gunzburger, M.D.1    Peterson, J.2    Shadid, J.N.3
  • 4
    • 0037481177 scopus 로고    scopus 로고
    • Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods
    • Meyer M., Matthies H.G. Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods. Comput. Mech. 2003, 31(1-2):179-191.
    • (2003) Comput. Mech. , vol.31 , Issue.1-2 , pp. 179-191
    • Meyer, M.1    Matthies, H.G.2
  • 5
    • 0023577190 scopus 로고
    • The reduced-basis method for initial value problems
    • Porsching T.A., Lee M.Y.L. The reduced-basis method for initial value problems. SIAM J. Numer. Anal. 1987, 24:1277-1287.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1277-1287
    • Porsching, T.A.1    Lee, M.Y.L.2
  • 6
    • 0020547404 scopus 로고
    • On the error behavior of the reduced basis technique for nonlinear finite element approximations
    • Fink J.P., Rheinboldt W.C. On the error behavior of the reduced basis technique for nonlinear finite element approximations. Z. Angew. Math. Mech. 1983, 63(1):21-28.
    • (1983) Z. Angew. Math. Mech. , vol.63 , Issue.1 , pp. 21-28
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 7
    • 0017970146 scopus 로고
    • Automatic choice of global shape functions in structural analysis
    • Almroth B.O., Stern P., Brogan F.A. Automatic choice of global shape functions in structural analysis. AIAA J. 1978, 16:525-528.
    • (1978) AIAA J. , vol.16 , pp. 525-528
    • Almroth, B.O.1    Stern, P.2    Brogan, F.A.3
  • 8
    • 0019242096 scopus 로고
    • Recent advances in reduction methods for nonlinear problems
    • Noor A.K. Recent advances in reduction methods for nonlinear problems. Comput. Struct. 1981, 13:31-44.
    • (1981) Comput. Struct. , vol.13 , pp. 31-44
    • Noor, A.K.1
  • 9
    • 53749107686 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
    • Rozza G., Huynh D.B.P., Patera A.T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Meth. Engrg. 2008, 15(3):229-275. .
    • (2008) Arch. Comput. Meth. Engrg. , vol.15 , Issue.3 , pp. 229-275
    • Rozza, G.1    Huynh, D.B.P.2    Patera, A.T.3
  • 10
    • 79952244756 scopus 로고    scopus 로고
    • High-Fidelity Real-Time Simulation on Deployed Platforms, Computers and Fluids Specail issue. in: Proceedings of the Symposium on High Accuracy Flow Simulations (HAFS), École Polytechnique Fédérale de Lausanne, February 15-16, 2010. Available from:
    • D.B.P. Huynh, D.J. Knezevic, J.W. Peterson, A.T. Patera, High-Fidelity Real-Time Simulation on Deployed Platforms, Computers and Fluids Specail issue. in: Proceedings of the Symposium on High Accuracy Flow Simulations (HAFS), École Polytechnique Fédérale de Lausanne, February 15-16, 2010. Available from: http://dx.doi.org/10.1016/j.compfluid.2010.07.007.
    • Huynh, D.B.P.1    Knezevic, D.J.2    Peterson, J.W.3    Patera, A.T.4
  • 11
    • 15744385753 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
    • Grepl M.A., Patera A.T. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. M2AN (Math. Model. Numer. Anal.) 2005, 39(1):157-181.
    • (2005) M2AN (Math. Model. Numer. Anal.) , vol.39 , Issue.1 , pp. 157-181
    • Grepl, M.A.1    Patera, A.T.2
  • 12
    • 85088184409 scopus 로고    scopus 로고
    • 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, 2003, paper 2003-3847.
    • K. Veroy, C. Prud'homme, D.V. Rovas, 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, 2003, paper 2003-3847.
    • Veroy, K.1    UPrud'homme, C.2    Rovas, D.V.3    Patera, A.T.4
  • 13
    • 77951147428 scopus 로고    scopus 로고
    • Parametric free-form shape design with PDE models and reduced basis method
    • Lassila T., Rozza G. Parametric free-form shape design with PDE models and reduced basis method. Comput. Meth. Appl. Mech. Engrg. 2010, 199(23-24):1583-1592. http://dx.doi.org/10.1016/j.cma.2010.01.007
    • (2010) Comput. Meth. Appl. Mech. Engrg. , vol.199 , Issue.23-24 , pp. 1583-1592
    • Lassila, T.1    Rozza, G.2
  • 14
    • 55049084619 scopus 로고    scopus 로고
    • A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems
    • Liu G.R., Zaw K., Wang Y.Y., Deng B. A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems. Comput. Meth. Appl. Mech. Engrg. 2008, 198(2):269-279. .
    • (2008) Comput. Meth. Appl. Mech. Engrg. , vol.198 , Issue.2 , pp. 269-279
    • Liu, G.R.1    Zaw, K.2    Wang, Y.Y.3    Deng, B.4
  • 15
    • 43149123393 scopus 로고    scopus 로고
    • LibMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
    • Kirk B.S., Peterson J.W., Stogner R.M., Carey G.F. LibMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations. Engrg. Comput. 2006, 23(3-4):237-254.
    • (2006) Engrg. Comput. , vol.23 , Issue.3-4 , pp. 237-254
    • Kirk, B.S.1    Peterson, J.W.2    Stogner, R.M.3    Carey, G.F.4
  • 16
    • 0002515487 scopus 로고    scopus 로고
    • Efficient management of parallelism in object oriented numerical software libraries
    • Birkhäuser Press, E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.)
    • Balay S., Eijkhout V., Gropp W.D., McInnes L.C., Smith B.F. Efficient management of parallelism in object oriented numerical software libraries. Modern Software Tools in Scientific Computing 1997, 163-202. Birkhäuser Press. E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.).
    • (1997) Modern Software Tools in Scientific Computing , pp. 163-202
    • Balay, S.1    Eijkhout, V.2    Gropp, W.D.3    McInnes, L.C.4    Smith, B.F.5
  • 17
    • 33745196196 scopus 로고    scopus 로고
    • SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
    • Hernandez V., Roman J.E., Vidal V. SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 2005, 31(3):351-362.
    • (2005) ACM Trans. Math. Softw. , vol.31 , Issue.3 , pp. 351-362
    • Hernandez, V.1    Roman, J.E.2    Vidal, V.3
  • 18
    • 36148955493 scopus 로고    scopus 로고
    • A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants
    • Huynh D.B.P., Rozza G., Sen S., Patera A.T. A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C. R. Acad. Sci. Paris, Série I 2007, 345(8):473-478.
    • (2007) C. R. Acad. Sci. Paris, Série I , vol.345 , Issue.8 , pp. 473-478
    • Huynh, D.B.P.1    Rozza, G.2    Sen, S.3    Patera, A.T.4
  • 19
    • 41549118036 scopus 로고    scopus 로고
    • Reduced basis method for finite volume approximations of parametrized evolution equations
    • Haasdonk B., Ohlberger M. Reduced basis method for finite volume approximations of parametrized evolution equations. M2AN (Math. Model. Numer. Anal.) 2008, 42(2):277-302.
    • (2008) M2AN (Math. Model. Numer. Anal.) , vol.42 , Issue.2 , pp. 277-302
    • Haasdonk, B.1    Ohlberger, M.2
  • 20
    • 70349560243 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers' equation
    • Nguyen N.C., Rozza G., Patera A.T. Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers' equation. Calcolo 2009, 46(3):157-185. .
    • (2009) Calcolo , vol.46 , Issue.3 , pp. 157-185
    • Nguyen, N.C.1    Rozza, G.2    Patera, A.T.3
  • 21
    • 15744385841 scopus 로고    scopus 로고
    • An "empirical interpolation" method: application to efficient reduced-basis discretization of partial differential equations
    • Barrault M., Maday Y., Nguyen N.C., Patera A.T. An "empirical interpolation" method: application to efficient reduced-basis discretization of partial differential equations. C. R. Acad. Sci. Paris, Série I 2004, 339:667-672.
    • (2004) C. R. Acad. Sci. Paris, Série I , vol.339 , pp. 667-672
    • Barrault, M.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 23
    • 15744406041 scopus 로고    scopus 로고
    • Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations; Rigorous reduced-basis a posteriori error bounds
    • Veroy K., Patera A.T. Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations; Rigorous reduced-basis a posteriori error bounds. Int. J. Numer. Meth. Fluids 2005, 47:773-788.
    • (2005) Int. J. Numer. Meth. Fluids , vol.47 , pp. 773-788
    • Veroy, K.1    Patera, A.T.2
  • 24
    • 79952036896 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations, Preprint, Mathematical Models and Methods in Applied Sciences, accepted for publication. Available from:
    • D.J. Knezevic, N.C. Nguyen, A.T. Patera, Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations, Preprint, Mathematical Models and Methods in Applied Sciences, accepted for publication. Available from: >http://augustine.mit.edu/methodology/papers/atp_M3AS_preprint_Nov09.pdf.
    • Knezevic, D.J.1    Nguyen, N.C.2    Patera, A.T.3
  • 25
    • 54949153748 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for many-parameter heat conduction problems
    • Sen S. Reduced basis approximation and a posteriori error estimation for many-parameter heat conduction problems. Numer. Heat Transfer, Part B: Fundam. 2008, 54(5):369-389.
    • (2008) Numer. Heat Transfer, Part B: Fundam. , vol.54 , Issue.5 , pp. 369-389
    • Sen, S.1
  • 26
    • 67650149648 scopus 로고    scopus 로고
    • Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
    • Geuzaine C., Remacle J.-F. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Meth. Engrg. 2009, 79(11):1309-1331.
    • (2009) Int. J. Numer. Meth. Engrg. , vol.79 , Issue.11 , pp. 1309-1331
    • Geuzaine, C.1    Remacle, J.-F.2
  • 28
    • 79952038938 scopus 로고    scopus 로고
    • Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: version 5.0 user's manual, Sandia technical report SAND2010-2183
    • B. Adams, W. Bohnhoff, K. Dalbey, J. Eddy, M. Eldred, D. Gay, K. Haskell, P. Hough, L. Swiler, Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: version 5.0 user's manual, Sandia technical report SAND2010-2183, 2009.
    • (2009)
    • Adams, B.1    Bohnhoff, W.2    Dalbey, K.3    Eddy, J.4    Eldred, M.5    Gay, D.6    Haskell, K.7    Hough, P.8    Swiler, L.9
  • 29
    • 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. Aerosp. Sci. 2001, 37(1):21-58.
    • (2001) Prog. Aerosp. Sci. , vol.37 , Issue.1 , pp. 21-58
    • Bewley, T.R.1
  • 30
    • 20544476549 scopus 로고
    • Aerodynamic design via control theory
    • Jameson A. Aerodynamic design via control theory. J. Sci. Comput. 1988, 3:233-260.
    • (1988) J. Sci. Comput. , vol.3 , pp. 233-260
    • Jameson, A.1
  • 31
    • 0000104411 scopus 로고    scopus 로고
    • A reduced-order method for simulation and control of fluid flows
    • Ito K., Ravindran S.S. A reduced-order method for simulation and control of fluid flows. J. Comput. Phys. 1998, 143(2):403-425.
    • (1998) J. Comput. Phys. , vol.143 , Issue.2 , pp. 403-425
    • Ito, K.1    Ravindran, S.S.2
  • 32
    • 78651554414 scopus 로고    scopus 로고
    • An hp Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations
    • Eftang J.L., Patera A.T., Rønquist E.M. An hp Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations. SIAM J. Sci. Comp. 2010, 32(6):3170-3200.
    • (2010) SIAM J. Sci. Comp. , vol.32 , Issue.6 , pp. 3170-3200
    • Eftang, J.L.1    Patera, A.T.2    Rønquist, E.M.3
  • 33
    • 79952043132 scopus 로고    scopus 로고
    • An hp certified reduced basis method for parametrized time-dependent partial differential equations, MCMDS, Accepted for publication.
    • J.L. Eftang, D.J. Knezevic, A.T. Patera, E.M. Rønquist, An hp certified reduced basis method for parametrized time-dependent partial differential equations, MCMDS, Accepted for publication.
    • Eftang, J.L.1    Knezevic, D.J.2    Patera, A.T.3    Rønquist, E.M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.