메뉴 건너뛰기




Volumn 13, Issue 1, 2014, Pages 339-365

Construction of bifurcation diagrams using POD on the fly

Author keywords

Adaptive methods; Bifurcation diagrams; Complex Ginzburg Landau equation; Galerkin projection; Poincar maps; Proper orthogonal decomposition; Reduced order models

Indexed keywords

CHAOS THEORY; GALERKIN METHODS; GRAPHIC METHODS; NUMERICAL METHODS; PRINCIPAL COMPONENT ANALYSIS;

EID: 84897034749     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/130927267     Document Type: Article
Times cited : (28)

References (55)
  • 1
    • 0141737698 scopus 로고    scopus 로고
    • Symbolic-numerical methods for the computation of normal forms of pdes
    • M. Ahamadi and J.-J. Gervais, Symbolic-numerical methods for the computation of normal forms of PDEs, J. Comput. Appl. Math., 158 (2003), pp. 443-472.
    • (2003) J. Comput. Appl. Math , vol.158 , pp. 443-472
    • Ahamadi, M.1    Gervais, J.-J.2
  • 2
    • 0142010087 scopus 로고    scopus 로고
    • Introduction to numerical continuation methods classics
    • SIAM, Philadelphia
    • E. L. Allgower and K. Georg, Introduction to Numerical Continuation Methods, Classics Appl. Math. 45, SIAM, Philadelphia, 2003.
    • Appl. Math , vol.45 , pp. 2003
    • Allgower, E.L.1    Georg, K.2
  • 3
    • 77957171943 scopus 로고    scopus 로고
    • Reduced order model for viscous aerodynamic flow past an airfoil
    • D. Alonso, J. M. Vega, and A. Velazquez, Reduced order model for viscous aerodynamic flow past an airfoil, AIAA J., 48 (2010), pp. 1946-1958.
    • (2010) AIAA J , vol.48 , pp. 1946-1958
    • Alonso, D.1    Vega, J.M.2    Velazquez, A.3
  • 4
    • 84860624990 scopus 로고    scopus 로고
    • Reduced-order modeling of threedimensional external aerodynamic flows
    • D. Alonso, J. M. Vega, A. Velazquez, and V. de Pablo, Reduced-order modeling of threedimensional external aerodynamic flows, J. Aerospace Engrg., 25 (2012), pp. 588-599.
    • (2012) J. Aerospace Engrg , vol.25 , pp. 588-599
    • Alonso, D.1    Vega, J.M.2    Velazquez, A.3    De Pablo, V.4
  • 5
    • 65849119296 scopus 로고    scopus 로고
    • A method to generate computationally efficient reduced order models
    • D. Alonso, A. Velazquez, and J. M. Vega, A method to generate computationally efficient reduced order models, Comput. Methods Appl. Mech. Engrg., 198 (2009), pp. 2683-2691.
    • (2009) Comput. Methods Appl. Mech. Engrg , vol.198 , pp. 2683-2691
    • Alonso, D.1    Velazquez, A.2    Vega, J.M.3
  • 6
    • 0036013603 scopus 로고    scopus 로고
    • The world of the complex ginzburg-landau equation
    • I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Rev. Modern Phys., 74 (2002), pp. 100-142.
    • (2002) Rev. Modern Phys , vol.74 , pp. 100-142
    • Aranson, I.S.1    Kramer, L.2
  • 7
    • 77957833609 scopus 로고    scopus 로고
    • Model reduction in the back step fluid-thermal problem with variable geometry
    • E. Bache, J. M. Vega, and A. Velazquez, Model reduction in the back step fluid-thermal problem with variable geometry, Int. J. Thermal Sci., 49 (2010), pp. 2376-2384.
    • (2010) Int. J. Thermal Sci , vol.49 , pp. 2376-2384
    • Bache, E.1    Vega, J.M.2    Velazquez, A.3
  • 8
    • 84884595115 scopus 로고    scopus 로고
    • Low-dimensional modelling of high-reynoldsnumber shear flows incorporating constraints from the navier-stokes equation
    • M. J. Balajewicz, E. H. Dowell, and B. R. Noack, Low-dimensional modelling of high-Reynoldsnumber shear flows incorporating constraints from the Navier-Stokes equation, J. Fluid Mech., 729 (2013), pp. 285-308.
    • (2013) J. Fluid Mech , vol.729 , pp. 285-308
    • Balajewicz, M.J.1    Dowell, E.H.2    Noack, B.R.3
  • 13
    • 84864451333 scopus 로고    scopus 로고
    • Adaptive reduced-order-model-based control-law design for active flutter suppression
    • G. Chen, J. Sun, and Y.-M. Li, Adaptive reduced-order-model-based control-law design for active flutter suppression, J. Aircraft, 49 (2012), pp. 973-980.
    • (2012) J. Aircraft , vol.49 , pp. 973-980
    • Chen, G.1    Sun, J.2    Li, Y.-M.3
  • 15
    • 18344390422 scopus 로고    scopus 로고
    • Calibrated reduced-order pod-galerkin system for fluid flow modelling
    • M. Couplet, C. Basdevant, and P. Sagaut, Calibrated reduced-order POD-Galerkin system for fluid flow modelling, J. Comput. Phys., 207 (2005), pp. 192-220.
    • (2005) J. Comput. Phys , vol.207 , pp. 192-220
    • Couplet, M.1    Basdevant, C.2    Sagaut, P.3
  • 16
    • 0003078274 scopus 로고
    • Symmetry and symmetry-breaking bifurcations in fluid dynamics
    • J. D. Crawford and E. Knobloch, Symmetry and symmetry-breaking bifurcations in fluid dynamics, Annu. Rev. Fluid Mech., 23 (1991), pp. 341-387.
    • (1991) Annu. Rev. Fluid Mech , vol.23 , pp. 341-387
    • Crawford, J.D.1    Knobloch, E.2
  • 19
    • 0034965813 scopus 로고    scopus 로고
    • Modeling of fluid-structure interaction
    • E. H. Dowell and K. C. Hall, Modeling of fluid-structure interaction, Annu. Rev. Fluid Mech., 33 (2001), pp. 445-490.
    • (2001) Annu. Rev. Fluid Mech , vol.33 , pp. 445-490
    • Dowell, E.H.1    Hall, K.C.2
  • 20
    • 0001047390 scopus 로고
    • Inertial manifolds for the kuramoto-sivashinsky equation and an estimate of their lowest dimension
    • C. Foias, B. Nicolaenko, G. R. Sell, and R. Temam, Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension, J. Math. Pures Appl. (9), 67 (1988), pp. 197-226.
    • (1988) J. Math. Pures Appl. , vol.9 , Issue.67 , pp. 197-226
    • Foias, C.1    Nicolaenko, B.2    Sell, G.R.3    Temam, R.4
  • 21
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolution equations
    • C. Foias, G. R. Sell, and R. Temam, Inertial manifolds for nonlinear evolution equations, J. Differential Equations, 73 (1988), pp. 309-353.
    • (1988) J. Differential Equations , vol.73 , pp. 309-353
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 23
    • 27844579108 scopus 로고    scopus 로고
    • Weakly nonlinear and numerical analyses of dynamics in a solid combustion model
    • L. K. Gross and J. Yu, Weakly nonlinear and numerical analyses of dynamics in a solid combustion model, SIAM J. Appl. Math., 65 (2005), pp. 1708-1725.
    • (2005) SIAM J. Appl. Math , vol.65 , pp. 1708-1725
    • Gross, L.K.1    Yu, J.2
  • 25
    • 84874767568 scopus 로고    scopus 로고
    • Computation of hopf bifurcations coupling reduced order models and the asymptotic numerical method
    • J. Heyman, G. Girault, Y. Guevel, C. Allery, A. Hamdouni, and J. M. Cadou, Computation of Hopf bifurcations coupling reduced order models and the asymptotic numerical method, Comput. & Fluids, 76 (2013), pp. 73-85.
    • (2013) Comput. & Fluids , vol.76 , pp. 73-85
    • Heyman, J.1    Girault, G.2    Guevel, Y.3    Allery, C.4    Hamdouni, A.5    Cadou, J.M.6
  • 27
    • 84897090736 scopus 로고    scopus 로고
    • Secondary bifurcation in a two-dimensional flow past a square cylinder
    • to appear
    • V. L. Kalb and A. E. Deane, Secondary bifurcation in a two-dimensional flow past a square cylinder, Phys. Fluids, to appear.
    • Phys. Fluids
    • Kalb, V.L.1    Deane, A.E.2
  • 28
    • 24944545967 scopus 로고    scopus 로고
    • Elements of applied bifurcation theory
    • Springer-Verlag, New York
    • Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Appl. Math. Sci. 112, Springer-Verlag, New York, 2004.
    • (2004) Appl. Math. Sci , vol.112
    • Kuznetsov, Y.A.1
  • 30
    • 33745335814 scopus 로고    scopus 로고
    • Reduced-order fluid/structure modeling of a complete aircraft configuration
    • T. Lieu, C. Farhat, and M. Lesoinne, Reduced-order fluid/structure modeling of a complete aircraft configuration, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 5730-5742.
    • (2006) Comput. Methods Appl. Mech. Engrg , vol.195 , pp. 5730-5742
    • Lieu, T.1    Farhat, C.2    Lesoinne, M.3
  • 31
    • 84875208775 scopus 로고    scopus 로고
    • Efficient computation of the pod manifold containing the information required to generate a multi-parameter aerodynamic database
    • L. S. Lorente, J. M. Vega, and A. Velazquez, Efficient computation of the POD manifold containing the information required to generate a multi-parameter aerodynamic database, Aerosp. Sci. Technol., 25 (2013), pp. 152-160.
    • (2013) Aerosp. Sci. Technol , vol.25 , pp. 152-160
    • Lorente, L.S.1    Vega, J.M.2    Velazquez, A.3
  • 33
    • 1342283898 scopus 로고    scopus 로고
    • Reduced-order modelling: New approaches for computations physics
    • D. J. Lucia, P. S. Beran, and W. A. Silva, Reduced-order modelling: New approaches for computations physics, Prog. Aerosp. Sci., 40 (2004), pp. 51-117.
    • (2004) Prog. Aerosp. Sci , vol.40 , pp. 51-117
    • Lucia, D.J.1    Beran, P.S.2    Silva, W.A.3
  • 34
    • 0347053767 scopus 로고    scopus 로고
    • Dynamics of counter-propagating waves in parametrically forced systems
    • C. Martel, E. Knobloch, and J. M. Vega, Dynamics of counter-propagating waves in parametrically forced systems, Phys. D, 137 (2000), pp. 94-123.
    • (2000) Phys , vol.D , Issue.137 , pp. 94-123
    • Martel, C.1    Knobloch, E.2    Vega, J.M.3
  • 35
    • 71749095955 scopus 로고    scopus 로고
    • Heat transfer enhancement in micro-channels caused by vortex promoters
    • M. Meis, F. Varas, A. Velazquez, and J. M. Vega, Heat transfer enhancement in micro-channels caused by vortex promoters, Int. J. Heat Mass Transfer, 53 (2010), pp. 29-40.
    • (2010) Int. J. Heat Mass Transfer , vol.53 , pp. 29-40
    • Meis, M.1    Varas, F.2    Velazquez, A.3    Vega, J.M.4
  • 36
    • 84884971265 scopus 로고    scopus 로고
    • Newton's method and symmetry for semilinear elliptic pde on the cube
    • J. M. Neuberger, N. Sieben, and J. W. Swift, Newton's method and symmetry for semilinear elliptic PDE on the cube, SIAM J. Appl. Dyn. Syst., 12 (2013), pp. 1237-1279.
    • (2013) SIAM J. Appl. Dyn. Syst , vol.12 , pp. 1237-1279
    • Neuberger, J.M.1    Sieben, N.2    Swift, J.W.3
  • 37
    • 0039175969 scopus 로고
    • Localization and approximation of attractors for the ginzburg-landau equation
    • K. Promislow and R. Temam, Localization and approximation of attractors for the Ginzburg-Landau equation, J. Dynam. Differential Equations, 3 (1991), pp. 491-514.
    • (1991) J. Dynam. Differential Equations , vol.3 , pp. 491-514
    • Promislow, K.1    Temam, R.2
  • 39
    • 77957171362 scopus 로고    scopus 로고
    • Reduced order models based on local pod plus galerkin projection
    • M. L. Raṕun and J. M. Vega, Reduced order models based on local POD plus Galerkin projection, J. Comput. Phys., 229 (2010), pp. 3046-3063.
    • (2010) J. Comput. Phys , vol.229 , pp. 3046-3063
    • Raṕun, M.L.1    Vega, J.M.2
  • 40
    • 0034343536 scopus 로고    scopus 로고
    • On low-dimensional galerkin models for fluid flow
    • D. Rempfer, On low-dimensional Galerkin models for fluid flow, Theor. Comput. Fluid Dyn., 14 (2000), pp. 75-88.
    • (2000) Theor. Comput. Fluid Dyn , vol.14 , pp. 75-88
    • Rempfer, D.1
  • 41
    • 0038814407 scopus 로고    scopus 로고
    • Low-dimensional modeling and numerical simulation of transition in simple shear flows
    • D. Rempfer, Low-dimensional modeling and numerical simulation of transition in simple shear flows, Annu. Rev. Fluid Mech., 35 (2003), pp. 229-265.
    • (2003) Annu. Rev. Fluid Mech , vol.35 , pp. 229-265
    • Rempfer, D.1
  • 42
    • 33847193223 scopus 로고    scopus 로고
    • An introduction to partial differential equations
    • Springer-Verlag, New York
    • M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, Texts Appl. Math. 13, Springer-Verlag, New York, 2004.
    • (2004) Texts Appl. Math , vol.13
    • Renardy, M.1    Rogers, R.C.2
  • 43
    • 60949099090 scopus 로고    scopus 로고
    • Hyper-reduction of mechanical models involving internal variables
    • D. Ryckelynck, Hyper-reduction of mechanical models involving internal variables, Internat. J. Numer. Methods Engrg., 77 (2009), pp. 75-89.
    • (2009) Internat. J. Numer. Methods Engrg , vol.77 , pp. 75-89
    • Ryckelynck, D.1
  • 44
    • 33750572430 scopus 로고    scopus 로고
    • Amplitude equations close to a triple-(+1) bifurcation point of d4-symmetric periodic orbits in o(2) equivariant systems
    • J. Sanchez, M. Net, and J. M. Vega, Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2) equivariant systems, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1357-1380.
    • (2006) Discrete Contin Dyn Syst Ser B , vol.6 , pp. 1357-1380
    • Sanchez, J.1    Net, M.2    Vega, J.M.3
  • 45
    • 84861647251 scopus 로고    scopus 로고
    • Numerical bifurcation study of superconducting patterns on a square
    • N. Schlomer, D. Avitabile, and W. Vanroose, Numerical bifurcation study of superconducting patterns on a square, SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 447-477.
    • (2012) SIAM J. Appl. Dyn. Syst , vol.11 , pp. 447-477
    • Schlomer, N.1    Avitabile, D.2    Vanroose, W.3
  • 46
    • 47949093987 scopus 로고    scopus 로고
    • Lowdimensional modelling of a transient cylinder wake using double proper orthogonal decomposition
    • S. G. Siegel, J. Seidel, C. Fagley, D. M. Luchtenburg, K. Cohen, and T. McLaughlin, Lowdimensional modelling of a transient cylinder wake using double proper orthogonal decomposition, J. Fluid Mech., 610 (2008), pp. 1-42.
    • (2008) J. Fluid Mech , vol.610 , pp. 1-42
    • Siegel, S.G.1    Seidel, J.2    Fagley, C.3    Luchtenburg, D.M.4    Cohen, K.5    McLaughlin, T.6
  • 47
    • 0842333833 scopus 로고    scopus 로고
    • A spectral viscosity method for correcting the long-term behavior of pod models
    • S. Sirisup and G. E. Karniadakis, A spectral viscosity method for correcting the long-term behavior of POD models, J. Comput. Phys., 194 (2004), pp. 92-116.
    • (2004) J. Comput. Phys , vol.194 , pp. 92-116
    • Sirisup, S.1    Karniadakis, G.E.2
  • 48
    • 16344386614 scopus 로고    scopus 로고
    • Stability and accuracy of periodic flow solutions obtained by a pod-penalty method
    • S. Sirisup and G. E. Karniadakis, Stability and accuracy of periodic flow solutions obtained by a POD-penalty method, Phys. D, 202 (2005), pp. 218-237.
    • (2005) Phys , vol.D , Issue.202 , pp. 218-237
    • Sirisup, S.1    Karniadakis, G.E.2
  • 49
    • 18844459925 scopus 로고    scopus 로고
    • Equation-free/galerkin-free podassisted computation of incompressible flows
    • S. Sirisup, G. E. Karniadakis, D. Xiu, and I. G. Kevrekidis, Equation-free/Galerkin-free PODassisted computation of incompressible flows, J. Comput. Phys., 207 (2005), pp. 568-587.
    • (2005) J. Comput. Phys , vol.207 , pp. 568-587
    • Sirisup, S.1    Karniadakis, G.E.2    Xiu, D.3    Kevrekidis, I.G.4
  • 50
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures
    • L. Sirovich, Turbulence and the dynamics of coherent structures, Quart. Appl. Math., 45 (1987), pp. 561-590.
    • (1987) Quart. Appl. Math , vol.45 , pp. 561-590
    • Sirovich, L.1
  • 51
    • 77953468682 scopus 로고    scopus 로고
    • Mean field representation of the natural and actuated cylinder wake
    • G. Tadmor, O. Lehmann, B. R. Noack, and M. Morzynski, Mean field representation of the natural and actuated cylinder wake, Phys. Fluids, 22 (2010), 034102.
    • (2010) Phys. Fluids , vol.22 , pp. 034102
    • Tadmor, G.1    Lehmann, O.2    Noack, B.R.3    Morzynski, M.4
  • 52
    • 84856551658 scopus 로고    scopus 로고
    • Local pod plus galerkin projection in the unsteady liddriven cavity problem
    • F. Terragni, E. Valero, and J. M. Vega, Local POD plus Galerkin projection in the unsteady liddriven cavity problem, SIAM J. Sci. Comput., 33 (2011), pp. 3538-3561.
    • (2011) SIAM J. Sci. Comput , vol.33 , pp. 3538-3561
    • Terragni, F.1    Valero, E.2    Vega, J.M.3
  • 53
    • 84863515624 scopus 로고    scopus 로고
    • On the use of pod-based roms to analyze bifurcations in some dissipative systems
    • F. Terragni and J. M. Vega, On the use of POD-based ROMs to analyze bifurcations in some dissipative systems, Phys. D, 241 (2012), pp. 1393-1405.
    • (2012) Phys , vol.241 D , pp. 1393-1405
    • Terragni, F.1    Vega, J.M.2
  • 54
    • 77049124832 scopus 로고    scopus 로고
    • Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver
    • J. P. Thomas, E. H. Dowell, and K. C. Hall, Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver, AIAA J., 48 (2010), pp. 19-24.
    • (2010) AIAA J , vol.48 , pp. 19-24
    • Thomas, J.P.1    Dowell, E.H.2    Hall, K.C.3
  • 55
    • 34548180387 scopus 로고    scopus 로고
    • Modulated surface waves in large aspect ratio, horizontally vibrated containers
    • F. Varas and J. M. Vega, Modulated surface waves in large aspect ratio, horizontally vibrated containers, J. Fluid Mech., 569 (2007), pp. 271-304.
    • (2007) J. Fluid Mech , vol.569 , pp. 271-304
    • Varas, F.1    Vega, J.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.