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Volumn 234, Issue 1, 2013, Pages 540-559

Non-linear petrov-galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods

Author keywords

Finite element; Petrov Galerkin; Proper orthogonal decomposition; Reduced order modelling; Shock wave

Indexed keywords

ADVECTION; FINITE ELEMENT METHOD; GALERKIN METHODS; NUMERICAL METHODS; PRINCIPAL COMPONENT ANALYSIS;

EID: 84870571331     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.10.011     Document Type: Article
Times cited : (72)

References (28)
  • 2
    • 33746082025 scopus 로고    scopus 로고
    • Efficiency of reduced-order, time-dependent adjoint data assimilation approaches
    • I. Hoteit, A. Kohl, Efficiency of reduced-order, time-dependent adjoint data assimilation approaches, J. Oceanogr. 62 (4) (2006) 539-550.
    • (2006) J. Oceanogr , vol.62 , Issue.4 , pp. 539-550
    • Hoteit, I.1    Kohl, A.2
  • 3
    • 33750450033 scopus 로고    scopus 로고
    • Model-reduced variational data assimilation
    • P.T.M. Vermeulen, A.W. Heemink, Model-reduced variational data assimilation, Mon. Wea. Rev. 134 (2006) 2888-2899.
    • (2006) Mon. Wea. Rev. , vol.134 , pp. 2888-2899
    • Vermeulen, P.T.M.1    Heemink, A.W.2
  • 4
    • 38549084232 scopus 로고    scopus 로고
    • Reduced-order 4d-var: a preconditioner for the incremental 4d-var data assimilation method
    • L18609-1-4
    • C. Robert, E. Blayo, J. Verron, J. Blum, F.X. Le Dimet, Reduced-order 4d-var: a preconditioner for the incremental 4d-var data assimilation method, Geophys. Res. Lett. 33 (2006). pp. L18609-1-4.
    • (2006) Geophys. Res. Lett. , vol.33
    • Robert, C.1    Blayo, E.2    Verron, J.3    Blum, J.4    Le Dimet, F.X.5
  • 5
    • 0004160422 scopus 로고    scopus 로고
    • Approximation of Large-scale Dynamical Systems, Book Series
    • DC 06, SIAM, Philadelphia
    • A.C. Antoulas, Approximation of Large-scale Dynamical Systems, Book Series: Advances in Design and Control, DC 06, SIAM, Philadelphia, 2005.
    • (2005) Advances in Design and Control
    • Antoulas, A.C.1
  • 6
    • 0037322638 scopus 로고    scopus 로고
    • A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
    • M. Rewienski, J. White, A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 22 (2) (2003) 155-170.
    • (2003) IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. , vol.22 , Issue.2 , pp. 155-170
    • Rewienski, M.1    White, J.2
  • 7
    • 0036849510 scopus 로고    scopus 로고
    • Balanced model reduction via the proper orthogonal decomposition
    • K. Willcox, J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA J. 40 (11) (2002) 2323-2330.
    • (2002) AIAA J , vol.40 , Issue.11 , pp. 2323-2330
    • Willcox, K.1    Peraire, J.2
  • 8
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • F. Bassi, S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comput. Phys. 131 (1997) 267-279.
    • (1997) J. Comput. Phys. , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 10
    • 62849111900 scopus 로고    scopus 로고
    • A POD reduced order unstructured mesh ocean modelling method for moderate Reynolds number flows
    • F. Fang, C.C. Pain, I.M. Navon, M.D. Piggott, G.J. Gorman, P. Allison, A.J.H. Goddard, A POD reduced order unstructured mesh ocean modelling method for moderate Reynolds number flows, Ocean Model. 28 (1-3) (2009) 127-136.
    • (2009) Ocean Model , vol.28 , Issue.1-3 , pp. 127-136
    • Fang, F.1    Pain, C.C.2    Navon, I.M.3    Piggott, M.D.4    Gorman, G.J.5    Allison, P.6    Goddard, A.J.H.7
  • 11
    • 0034400382 scopus 로고    scopus 로고
    • Stability properties of POD-Galerkin approximations for the compressible Navier-Stokes equations
    • A.Iollo, S. Lanteri, J.A. Desideri, Stability properties of POD-Galerkin approximations for the compressible Navier-Stokes equations, Theor. Comput. Fluid Dyn. 13 (2000) 377-396.
    • (2000) Theor. Comput. Fluid Dyn. , vol.13 , pp. 377-396
    • Iollo, A.1    Lanteri, S.2    Desideri, J.A.3
  • 12
    • 1842688147 scopus 로고    scopus 로고
    • Low-order modelling of laminar flow regimes past a confined square cylinder
    • B.Galletti, C.H. Bruneau, L.Zannetti, A. Iollo, Low-order modelling of laminar flow regimes past a confined square cylinder, J. Fluid Mech. 503 (2004)161-170.
    • (2004) J. Fluid Mech , vol.503 , pp. 161-170
    • Galletti, B.1    Bruneau, C.H.2    Zannetti, L.3    Iollo, A.4
  • 15
    • 53749102512 scopus 로고    scopus 로고
    • An efficient reduced-order modeling approach for non-linear parametrized partial differential equations
    • N.C. Nguyen, J. Peraire, An efficient reduced-order modeling approach for non-linear parametrized partial differential equations, Int. J. Numer. Methods Eng. 76 (2008) 27-55.
    • (2008) Int. J. Numer. Methods Eng. , vol.76 , pp. 27-55
    • Nguyen, N.C.1    Peraire, J.2
  • 16
    • 79952654642 scopus 로고    scopus 로고
    • Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
    • K. Carlberg, C. Bou-Mosleh, C. Farhat, Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations, Int. J. Numer. Methods Eng. 86 (2011) 155-181.
    • (2011) Int. J. Numer. Methods Eng , vol.86 , pp. 155-181
    • Carlberg, K.1    Bou-Mosleh, C.2    Farhat, C.3
  • 18
    • 0038625260 scopus 로고    scopus 로고
    • Optimal control of flow with discontinuities
    • Chris Homescu, I.M. Navon, Optimal control of flow with discontinuities, J. Comput. Phys. 187 (2003) 660-682.
    • (2003) J. Comput. Phys. , vol.187 , pp. 660-682
    • Homescu, C.1    Navon, I.M.2
  • 19
    • 79952440061 scopus 로고    scopus 로고
    • Riemann boundary conditions for the Boltzmann transport equation using arbitrary angular approximations
    • A.G. Buchan, S.R. Merton, C.C. Pain, R.P. Smedley-Stevenson, Riemann boundary conditions for the Boltzmann transport equation using arbitrary angular approximations, Ann. Nucl. Energy 38 (2011) 1186-1195.
    • (2011) Ann. Nucl. Energy , vol.38 , pp. 1186-1195
    • Buchan, A.G.1    Merton, S.R.2    Pain, C.C.3    Smedley-Stevenson, R.P.4
  • 21
    • 2942705023 scopus 로고
    • Survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
    • G.A. Sod, Survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys. 27 (1978) 1-31.
    • (1978) J. Comput. Phys. , vol.27 , pp. 1-31
    • Sod, G.A.1
  • 22
    • 0041087946 scopus 로고    scopus 로고
    • Remarks on the Approximation of the Euler Equations by a Low Order Model
    • A. Iollo, Remarks on the Approximation of the Euler Equations by a Low Order Model, INRIA, Report of research, RR-3329, 1997.
    • (1997) INRIA, Report of research , pp. 3329
    • Iollo, A.1
  • 23
    • 13844250570 scopus 로고    scopus 로고
    • The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows
    • B.R. Noack, R. Papas, P. Monkewitz, The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows, J. Fluid Mech. 523 (2005) 339-366.
    • (2005) J. Fluid Mech. , vol.523 , pp. 339-366
    • Noack, B.R.1    Papas, R.2    Monkewitz, P.3
  • 24
    • 0842279679 scopus 로고    scopus 로고
    • A hierarchy of low-dimensional models of the transient and post-transient cylinder wake
    • B.R. Noack, K. Afanasiev, M. Morzyński, G. Tadmor, F. Thiele, A hierarchy of low-dimensional models of the transient and post-transient cylinder wake, J. Fluid Mech. 497 (2003) 335-363.
    • (2003) J. Fluid Mech. , vol.497 , pp. 335-363
    • Noack, B.R.1    Afanasiev, K.2    Morzyński, M.3    Tadmor, G.4    Thiele, F.5
  • 26
    • 84861554455 scopus 로고    scopus 로고
    • Proper orthogonal decomposition closure models for turbulent flows a numerical comparison
    • Z. Wang, I. Akhtar, J. Borggaard, T. Iliescu, Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison, Comput. Methods Appl. Mech. Eng. 237-240 (2012) 10-26.
    • (2012) Comput. Methods Appl. Mech. Eng. , vol.237-240 , pp. 10-26
    • Wang, Z.1    Akhtar, I.2    Borggaard, J.3    Iliescu, T.4
  • 27
    • 0003542590 scopus 로고    scopus 로고
    • Riemann Solvers and Numerical Methods for Fluid Dynamics
    • Springer, Berlin, third ed
    • E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, A Practical Introduction, third ed., Springer, Berlin, 2009.
    • (2009) A Practical Introduction
    • Toro, E.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.