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Volumn 60, Issue , 2009, Pages 321-344

Equation-free multiscale computation: Algorithms and applications

Author keywords

Bifurcation analysis; Complex systems; Equation free methods; Patch dynamics; Simulation

Indexed keywords

ARSENALS; BIFURCATION (MATHEMATICS); COMPUTER AIDED ANALYSIS; DIFFERENTIAL EQUATIONS; LARGE SCALE SYSTEMS;

EID: 67449101766     PISSN: 0066426X     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.physchem.59.032607.093610     Document Type: Review
Times cited : (286)

References (150)
  • 5
    • 0037456891 scopus 로고    scopus 로고
    • Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems
    • Katsoulakis M, Majda A, Vlachos D. 2003. Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. J. Comput. Phys. 186:250-78
    • (2003) J. Comput. Phys , vol.186 , pp. 250-278
    • Katsoulakis, M.1    Majda, A.2    Vlachos, D.3
  • 7
    • 67651139948 scopus 로고    scopus 로고
    • Gaspard P. 1998. Chaos, Scattering and Statistical Mechanics. Cambridge: Cambridge Univ. Press
    • Gaspard P. 1998. Chaos, Scattering and Statistical Mechanics. Cambridge: Cambridge Univ. Press
  • 13
    • 67651104973 scopus 로고    scopus 로고
    • Keunings R. 2004. Micro-macro methods for the multiscale simulation of viscoelastic flows using molecular methods of kinetic theory. In Rheology Reviews, ed.DMBinding, KWalters, pp. 67-98. Aberystwyth, UK: Brit. Soc. Rheol.
    • Keunings R. 2004. Micro-macro methods for the multiscale simulation of viscoelastic flows using molecular methods of kinetic theory. In Rheology Reviews, ed.DMBinding, KWalters, pp. 67-98. Aberystwyth, UK: Brit. Soc. Rheol.
  • 14
    • 19944408985 scopus 로고    scopus 로고
    • From individual to collective behavior in bacterial chemotaxis
    • Erban R, Othmer HG. 2004. From individual to collective behavior in bacterial chemotaxis. SIAM J. Appl. Math. 65:361-91
    • (2004) SIAM J. Appl. Math , vol.65 , pp. 361-391
    • Erban, R.1    Othmer, H.G.2
  • 15
    • 4344590227 scopus 로고    scopus 로고
    • Generalized coarse-graining procedures for flow in porous media
    • Attinger S. 2003. Generalized coarse-graining procedures for flow in porous media. Comput. Geosci. 7:253-73
    • (2003) Comput. Geosci , vol.7 , pp. 253-273
    • Attinger, S.1
  • 16
    • 0034730149 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using time-steppers: A reaction-diffusion example
    • Theodoropoulos C, Qian YH, Kevrekidis IG. 2000. Coarse stability and bifurcation analysis using time-steppers: a reaction-diffusion example. Proc. Natl. Acad. Sci. USA 97:9840-45
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 9840-9845
    • Theodoropoulos, C.1    Qian, Y.H.2    Kevrekidis, I.G.3
  • 17
    • 85128858890 scopus 로고    scopus 로고
    • Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level tasks
    • Kevrekidis IG, Gear CW, Hyman JM, Kevrekidis PG, Runborg O, Theodoropoulos C. 2003. Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level tasks. Comm. Math. Sci. 1:715-62
    • (2003) Comm. Math. Sci , vol.1 , pp. 715-762
    • Kevrekidis, I.G.1    Gear, C.W.2    Hyman, J.M.3    Kevrekidis, P.G.4    Runborg, O.5    Theodoropoulos, C.6
  • 21
    • 77956688585 scopus 로고    scopus 로고
    • Nanomechanics of defects in solids
    • Ortiz M, Phillips R. 1999. Nanomechanics of defects in solids. Adv. Appl. Mech. 36:1-79
    • (1999) Adv. Appl. Mech , vol.36 , pp. 1-79
    • Ortiz, M.1    Phillips, R.2
  • 22
    • 0003159177 scopus 로고
    • Numerical Navier-Stokes solutions from gas-kinetic theory
    • Xu K, Prendergast KH. 1994. Numerical Navier-Stokes solutions from gas-kinetic theory. J. Comput. Phys. 114:9-17
    • (1994) J. Comput. Phys , vol.114 , pp. 9-17
    • Xu, K.1    Prendergast, K.H.2
  • 23
    • 0032509972 scopus 로고    scopus 로고
    • Connecting atomistic and mesoscale simulations of crystal plasticity
    • Bulatov V, Abraham FF, Kubin L, Devincre B, Yip S. 1998. Connecting atomistic and mesoscale simulations of crystal plasticity. Nature 391:669-72
    • (1998) Nature , vol.391 , pp. 669-672
    • Bulatov, V.1    Abraham, F.F.2    Kubin, L.3    Devincre, B.4    Yip, S.5
  • 24
    • 0032591725 scopus 로고    scopus 로고
    • Imposing field boundary conditions in MDsimulation of fluids: Optimal particle controller and buffer zone feedback
    • Li J, Liao D, Yip S. 1998. Imposing field boundary conditions in MDsimulation of fluids: optimal particle controller and buffer zone feedback. Mater. Res. Soc. Symp. Proc. 538:473-78
    • (1998) Mater. Res. Soc. Symp. Proc , vol.538 , pp. 473-478
    • Li, J.1    Liao, D.2    Yip, S.3
  • 25
    • 0002246664 scopus 로고    scopus 로고
    • Coupling continuum to molecular-dynamics simulation: Refiecting particle method and the field estimator
    • Li J, Liao D, Yip S. 1998. Coupling continuum to molecular-dynamics simulation: refiecting particle method and the field estimator. Phys. Rev. E 57:7259-67
    • (1998) Phys. Rev. E , vol.57 , pp. 7259-7267
    • Li, J.1    Liao, D.2    Yip, S.3
  • 26
    • 0034188113 scopus 로고    scopus 로고
    • Dynamic fracture of silicon: Concurrent simulation of quantum electrons, classical atoms, and the continuum solid
    • Abraham FF, Bernstein N, Broughton JQ, Hess D. 2000. Dynamic fracture of silicon: concurrent simulation of quantum electrons, classical atoms, and the continuum solid. Mater. Res. Soc. Bull. 25(5):27-32
    • (2000) Mater. Res. Soc. Bull , vol.25 , Issue.5 , pp. 27-32
    • Abraham, F.F.1    Bernstein, N.2    Broughton, J.Q.3    Hess, D.4
  • 28
    • 0001445852 scopus 로고    scopus 로고
    • A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method
    • Xu K. 2001. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. J. Comput. Phys. 171:289-335
    • (2001) J. Comput. Phys , vol.171 , pp. 289-335
    • Xu, K.1
  • 30
    • 0038579633 scopus 로고    scopus 로고
    • Atomistic/continuum coupling in computational materials science
    • Curtin WA, Miller RE. 2003. Atomistic/continuum coupling in computational materials science. Model. Simul. Mater. Sci. Eng. 11:R33-68
    • (2003) Model. Simul. Mater. Sci. Eng , vol.11
    • Curtin, W.A.1    Miller, R.E.2
  • 31
    • 0000580630 scopus 로고
    • Hybrid treatment of spatio-temporal behavior in surface reactions with coexisting immobile and highly mobile reactants
    • Tammaro M, Sabella M, Evans JW. 1995. Hybrid treatment of spatio-temporal behavior in surface reactions with coexisting immobile and highly mobile reactants. J. Chem. Phys. 103:10277-85
    • (1995) J. Chem. Phys , vol.103 , pp. 10277-10285
    • Tammaro, M.1    Sabella, M.2    Evans, J.W.3
  • 33
    • 0027608224 scopus 로고
    • Calculation of viscoelastic flow using molecular models: The CONNFFESSIT approach
    • Laso M, Öttinger HC. 1993. Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach. J. Non-Newton. Fluid Mech. 47:1-20
    • (1993) J. Non-Newton. Fluid Mech , vol.47 , pp. 1-20
    • Laso, M.1    Öttinger, H.C.2
  • 37
    • 0034724367 scopus 로고    scopus 로고
    • Optimal prediction and the Mori-Zwanzig representation of irreversible processes
    • Chorin AJ, Hald OH, Kupferman R. 2000. Optimal prediction and the Mori-Zwanzig representation of irreversible processes. Proc. Natl. Acad. Sci. USA 97:2968-73
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 2968-2973
    • Chorin, A.J.1    Hald, O.H.2    Kupferman, R.3
  • 40
    • 3042793188 scopus 로고    scopus 로고
    • Extracting macroscopic dynamics: Model problems and algorithms
    • Givon D, Kupferman R, Stuart A. 2004. Extracting macroscopic dynamics: model problems and algorithms. Nonlinearity 17:R55-127
    • (2004) Nonlinearity , vol.17
    • Givon, D.1    Kupferman, R.2    Stuart, A.3
  • 41
    • 0000514837 scopus 로고
    • Transport, collective motion and Brownian motion
    • Mori H. 1965. Transport, collective motion and Brownian motion. Prog. Theor. Phys. 33:423-50
    • (1965) Prog. Theor. Phys , vol.33 , pp. 423-450
    • Mori, H.1
  • 42
    • 18844402460 scopus 로고
    • Nonlinear generalized Langevin equations
    • Zwanzig R. 1973. Nonlinear generalized Langevin equations. J. Stat. Phys. 9:215-20
    • (1973) J. Stat. Phys , vol.9 , pp. 215-220
    • Zwanzig, R.1
  • 44
    • 2442444326 scopus 로고    scopus 로고
    • Extracting macroscopic stochastic dynamics: Model problems
    • Huisinga W, Schutte C, Stuart AM. 2003. Extracting macroscopic stochastic dynamics: model problems. Commun. Pure Appl. Math. 56:234-69
    • (2003) Commun. Pure Appl. Math , vol.56 , pp. 234-269
    • Huisinga, W.1    Schutte, C.2    Stuart, A.M.3
  • 45
    • 0000076283 scopus 로고    scopus 로고
    • A perturbation theory or ergodic Markov chains and application to numerical approximations
    • Shardlow T, Stuart AM. 2000. A perturbation theory or ergodic Markov chains and application to numerical approximations. SIAM J. Numer. Anal. 37:1120-37
    • (2000) SIAM J. Numer. Anal , vol.37 , pp. 1120-1137
    • Shardlow, T.1    Stuart, A.M.2
  • 46
    • 85128824735 scopus 로고    scopus 로고
    • Numerical techniques for multiscale dynamical systems with stochastic effects
    • Vanden-Eijnden E. 2003. Numerical techniques for multiscale dynamical systems with stochastic effects. Commun. Math. Sci. 1:377-84
    • (2003) Commun. Math. Sci , vol.1 , pp. 377-384
    • Vanden-Eijnden, E.1
  • 47
    • 27744467603 scopus 로고    scopus 로고
    • Analysis of numerical techniques for multiscale stochastic dynamical systems
    • E W, Liu D, Vanden-Eijnden E. 2005. Analysis of numerical techniques for multiscale stochastic dynamical systems. Commun. Pure Appl. Math. 58:1544-85
    • (2005) Commun. Pure Appl. Math , vol.58 , pp. 1544-1585
    • Liu, D.1    Vanden-Eijnden, E.2
  • 48
    • 0000383154 scopus 로고    scopus 로고
    • Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
    • Garcia AL, Bell JB, Crutchfield WY, Alder BJ. 1999. Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J. Comput. Phys. 154:134-55
    • (1999) J. Comput. Phys , vol.154 , pp. 134-155
    • Garcia, A.L.1    Bell, J.B.2    Crutchfield, W.Y.3    Alder, B.J.4
  • 50
    • 41349107349 scopus 로고    scopus 로고
    • Macroscopic dynamics through coarse-graining: A solvable example
    • Gorban AN, Karlin IV. 2002. Macroscopic dynamics through coarse-graining: a solvable example. Phys. Rev. E 65:026116
    • (2002) Phys. Rev. E , vol.65 , pp. 026116
    • Gorban, A.N.1    Karlin, I.V.2
  • 52
    • 4243756172 scopus 로고    scopus 로고
    • Ehrenfest's argument extended to a formalism of nonequilibrium thermodynamics
    • Gorban AN, Karlin IV, ÖttingerHC, Tatarinova LL. 2001. Ehrenfest's argument extended to a formalism of nonequilibrium thermodynamics. Phys. Rev. E 63:066124
    • (2001) Phys. Rev. E , vol.63 , pp. 066124
    • Gorban, A.N.1    Karlin, I.V.2    Öttinger, H.C.3    Tatarinova, L.L.4
  • 54
    • 67651129560 scopus 로고    scopus 로고
    • EW, Engquist B. 2003. The heterogeneous multiscale methods. Commun. Math. Sci. 1:87-132
    • EW, Engquist B. 2003. The heterogeneous multiscale methods. Commun. Math. Sci. 1:87-132
  • 55
    • 85150404232 scopus 로고    scopus 로고
    • EW, Engquist B, Li X, Ren W, Vanden-Eijnden E. 2007. Heterogeneous multiscale methods: a review. Commun. Comput. Phys. 2:367-450
    • EW, Engquist B, Li X, Ren W, Vanden-Eijnden E. 2007. Heterogeneous multiscale methods: a review. Commun. Comput. Phys. 2:367-450
  • 56
    • 0142096515 scopus 로고    scopus 로고
    • Multiscale scientiflc computation: Review 2001
    • ed, Berlin: Springer-Verlag
    • Brandt A. 2002. Multiscale scientiflc computation: review 2001. In Multiscale and Multiresolution Methods: Theory and Applications, ed. TJ Barth, T Chan, R Haimes, pp. 3-96. Berlin: Springer-Verlag
    • (2002) Multiscale and Multiresolution Methods: Theory and Applications , pp. 3-96
    • Brandt, A.1
  • 57
    • 67651106236 scopus 로고    scopus 로고
    • Holmes P, Lumley J, Berkooz G. 1996. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge: Cambridge Univ. Press
    • Holmes P, Lumley J, Berkooz G. 1996. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge: Cambridge Univ. Press
  • 58
    • 0001579586 scopus 로고
    • Coherent structures and chaos: A model problem
    • Sirovich L, Rodriguez J. 1987. Coherent structures and chaos: a model problem. Phys. Lett. A 120:211-14
    • (1987) Phys. Lett. A , vol.120 , pp. 211-214
    • Sirovich, L.1    Rodriguez, J.2
  • 59
    • 84896552867 scopus 로고    scopus 로고
    • Nonlinear model reduction for control distributed systems: A computer-assisted study
    • Shvartsman S, Kevrekidis IG. 1998. Nonlinear model reduction for control distributed systems: a computer-assisted study. AIChE J. 44:1579-95
    • (1998) AIChE J , vol.44 , pp. 1579-1595
    • Shvartsman, S.1    Kevrekidis, I.G.2
  • 60
    • 0029271077 scopus 로고
    • Surrogates for numerical simulations: Optimization of eddy-promoter heat exchangers
    • Yeşilyurt S, Patera A. 1995. Surrogates for numerical simulations: optimization of eddy-promoter heat exchangers. Comput. Methods Appl. Mech. Eng. 121:231-57
    • (1995) Comput. Methods Appl. Mech. Eng , vol.121 , pp. 231-257
    • Yeşilyurt, S.1    Patera, A.2
  • 61
    • 0033903648 scopus 로고    scopus 로고
    • Order reduction for nonlinear dynamic models of distributed reacting systems
    • Rico-Martinez R, Kevrekidis IG, Titi E. 2000. Order reduction for nonlinear dynamic models of distributed reacting systems. J. Process Control 10:177-84
    • (2000) J. Process Control , vol.10 , pp. 177-184
    • Rico-Martinez, R.1    Kevrekidis, I.G.2    Titi, E.3
  • 62
    • 0026067446 scopus 로고
    • Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders
    • Deane AE, Kevrekidis IG, Karniadakis GE, Orszag SA. 1991. Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys. Fluids A 3:2337-54
    • (1991) Phys. Fluids A , vol.3 , pp. 2337-2354
    • Deane, A.E.1    Kevrekidis, I.G.2    Karniadakis, G.E.3    Orszag, S.A.4
  • 63
    • 84972308308 scopus 로고
    • The dynamics of coherent structures in the wall region of a turbulent boundary layer
    • Aubry N, Holmes P, Lumley J, Stone E. 1988. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192:115-73
    • (1988) J. Fluid Mech , vol.192 , pp. 115-173
    • Aubry, N.1    Holmes, P.2    Lumley, J.3    Stone, E.4
  • 64
    • 0037104864 scopus 로고    scopus 로고
    • Coarse integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods
    • Gear CW, Kevrekidis IG, Theodoropoulos C. 2002. Coarse integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods. Comput. Chem. Eng. 26:941-63
    • (2002) Comput. Chem. Eng , vol.26 , pp. 941-963
    • Gear, C.W.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 65
    • 31744442265 scopus 로고    scopus 로고
    • Setayeshar S, Gear CW, Othmer HG, Kevrekidis IG. 2005. Application of coarse integration to bacterial chemotaxis. SIAM Multiscale Model. Simul. 4:307-27
    • Setayeshar S, Gear CW, Othmer HG, Kevrekidis IG. 2005. Application of coarse integration to bacterial chemotaxis. SIAM Multiscale Model. Simul. 4:307-27
  • 66
    • 0000240761 scopus 로고
    • Eine Theorie der photochemischen Reaktionsgeschwindigkeiten.
    • Bodenstein M. 1913. Eine Theorie der photochemischen Reaktionsgeschwindigkeiten. Z. Phys. Chem. 85:329-97
    • (1913) Z. Phys. Chem , vol.85 , pp. 329-397
    • Bodenstein, M.1
  • 67
    • 0037044961 scopus 로고    scopus 로고
    • Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice-gas model with lateral interactions
    • Makeev AG, Maroudas D, Panagiotopoulos AZ, Kevrekidis IG. 2002. Coarse bifurcation analysis of kinetic Monte Carlo simulations: a lattice-gas model with lateral interactions. J. Chem. Phys. 117:8229-40
    • (2002) J. Chem. Phys , vol.117 , pp. 8229-8240
    • Makeev, A.G.1    Maroudas, D.2    Panagiotopoulos, A.Z.3    Kevrekidis, I.G.4
  • 68
    • 0038608279 scopus 로고    scopus 로고
    • Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration and control via stochastic simulation
    • Siettos CI, Graham MD, Kevrekidis IG. 2003. Coarse Brownian dynamics for nematic liquid crystals: bifurcation, projective integration and control via stochastic simulation. J. Chem. Phys. 118:10149-57
    • (2003) J. Chem. Phys , vol.118 , pp. 10149-10157
    • Siettos, C.I.1    Graham, M.D.2    Kevrekidis, I.G.3
  • 69
    • 33646940952 scopus 로고
    • Numerical integration of the Cartesian equation of motion of a system with constraints: Molecular dynamics of n-alkanes
    • Ryckaert JP, Ciccotti G, Berendsen H. 1977. Numerical integration of the Cartesian equation of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comp. Phys. 23:327-41
    • (1977) J. Comp. Phys , vol.23 , pp. 327-341
    • Ryckaert, J.P.1    Ciccotti, G.2    Berendsen, H.3
  • 70
    • 16444385400 scopus 로고
    • Monte Carlo free energy estimation using non-Boltzmann sampling: Application to the subcritical Lennard Jones fluid
    • Torrie GM, Valleau JP. 1974. Monte Carlo free energy estimation using non-Boltzmann sampling: application to the subcritical Lennard Jones fluid. Chem. Phys. Lett. 28:578-81
    • (1974) Chem. Phys. Lett , vol.28 , pp. 578-581
    • Torrie, G.M.1    Valleau, J.P.2
  • 72
    • 24644483244 scopus 로고    scopus 로고
    • Coarse-grained numerical bifurcation analysis of lattice Boltzmann models
    • Van Leemput P, Lust K, Kevrekidis IG. 2005. Coarse-grained numerical bifurcation analysis of lattice Boltzmann models. Phys. D Nonlinear Phenom. 210:58-76
    • (2005) Phys. D Nonlinear Phenom , vol.210 , pp. 58-76
    • Van Leemput, P.1    Lust, K.2    Kevrekidis, I.G.3
  • 73
  • 74
    • 27144514794 scopus 로고    scopus 로고
    • Constraint-defined manifolds: A legacy code approach to lowdimensional computation
    • Gear CW, Kevrekidis IG. 2005. Constraint-defined manifolds: a legacy code approach to lowdimensional computation. J. Sci. Comput. 25:17-28
    • (2005) J. Sci. Comput , vol.25 , pp. 17-28
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 75
    • 67651116752 scopus 로고    scopus 로고
    • Analysis of the accuracy and convergence of equation-free projection to a slow manifold
    • In press
    • Zagaris A, Gear CW, Kaper T, Kevrekidis IG. 2008. Analysis of the accuracy and convergence of equation-free projection to a slow manifold. Math. Mod. Numer. Anal. In press
    • (2008) Math. Mod. Numer. Anal
    • Zagaris, A.1    Gear, C.W.2    Kaper, T.3    Kevrekidis, I.G.4
  • 76
    • 67651143003 scopus 로고    scopus 로고
    • Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold
    • Submitted manuscript
    • Zagaris A, Vandekerckhove C, Gear CW, Kaper T, Kevrekidis IG. 2008. Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold. Submitted manuscript
    • (2008)
    • Zagaris, A.1    Vandekerckhove, C.2    Gear, C.W.3    Kaper, T.4    Kevrekidis, I.G.5
  • 77
    • 55249111830 scopus 로고    scopus 로고
    • Mesoscale analysis of the equation-free constrained runs initialization scheme
    • Van Leemput P, Vanroose W, Roose D. 2007. Mesoscale analysis of the equation-free constrained runs initialization scheme. Multiscale Model. Simul. 6:1234-55
    • (2007) Multiscale Model. Simul , vol.6 , pp. 1234-1255
    • Van Leemput, P.1    Vanroose, W.2    Roose, D.3
  • 78
    • 67651136621 scopus 로고    scopus 로고
    • An efficient Newton-Krylov implementation of the constrained runs scheme for initializing on a slow manifold
    • In press
    • Vandekerckhove C, Roose D, Kevrekidis IG. 2008. An efficient Newton-Krylov implementation of the constrained runs scheme for initializing on a slow manifold. J. Sci. Comput. In press
    • (2008) J. Sci. Comput
    • Vandekerckhove, C.1    Roose, D.2    Kevrekidis, I.G.3
  • 79
    • 0027641824 scopus 로고
    • Stabilization of unstable procedures: The recursive projection method
    • Shroff GM, Keller HB. 1993. Stabilization of unstable procedures: the recursive projection method. SIAM J. Numer. Anal. 30:1099-120
    • (1993) SIAM J. Numer. Anal , vol.30 , pp. 1099-1120
    • Shroff, G.M.1    Keller, H.B.2
  • 80
    • 0001639797 scopus 로고    scopus 로고
    • An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions
    • Lust K, Roose D, Spence A, Champneys AR. 1998. An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions. SIAM J. Sci. Comput. 19:1188-209
    • (1998) SIAM J. Sci. Comput , vol.19 , pp. 1188-1209
    • Lust, K.1    Roose, D.2    Spence, A.3    Champneys, A.R.4
  • 81
    • 0037162264 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples
    • Makeev AG, Maroudas D, Kevrekidis IG. 2002. Coarse stability and bifurcation analysis using stochastic simulators: kinetic Monte Carlo examples. J. Chem. Phys. 116:10083-91
    • (2002) J. Chem. Phys , vol.116 , pp. 10083-10091
    • Makeev, A.G.1    Maroudas, D.2    Kevrekidis, I.G.3
  • 82
    • 3242788649 scopus 로고    scopus 로고
    • From molecular dynamics to coarse self-similar solutions: A simple example using equation-free computation
    • Chen L, Debenedetti P, Gear CW, Kevrekidis IG. 2004. From molecular dynamics to coarse self-similar solutions: a simple example using equation-free computation. J. Non-Newton. Fluid Mech. 120:215-23
    • (2004) J. Non-Newton. Fluid Mech , vol.120 , pp. 215-223
    • Chen, L.1    Debenedetti, P.2    Gear, C.W.3    Kevrekidis, I.G.4
  • 83
    • 0000015457 scopus 로고    scopus 로고
    • Effective bifurcation analysis: A time-stepper based approach
    • Runborg O, Theodoropoulos C, Kevrekidis IG. 2002. Effective bifurcation analysis: a time-stepper based approach. Nonlinearity 15:491-511
    • (2002) Nonlinearity , vol.15 , pp. 491-511
    • Runborg, O.1    Theodoropoulos, C.2    Kevrekidis, I.G.3
  • 85
    • 0346479606 scopus 로고    scopus 로고
    • Reconstruction equations and the Karhunen-Loéve expansion for systems with symmetry
    • Rowley C, Marsden J. 2000. Reconstruction equations and the Karhunen-Loéve expansion for systems with symmetry. Phys. D Nonlinear Phenom. 142:1-19
    • (2000) Phys. D Nonlinear Phenom , vol.142 , pp. 1-19
    • Rowley, C.1    Marsden, J.2
  • 88
    • 0012163533 scopus 로고
    • Numerical renormalization-group calculations for similarity solutions and traveling waves
    • Chen L, Goldenfeld N. 1995. Numerical renormalization-group calculations for similarity solutions and traveling waves. Phys. Rev. E 51:5577-81
    • (1995) Phys. Rev. E , vol.51 , pp. 5577-5581
    • Chen, L.1    Goldenfeld, N.2
  • 89
    • 0035877198 scopus 로고    scopus 로고
    • Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers
    • Lehoucq RB, Salinger AG. 2001. Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers. Int. J. Numer. Methods Fluids 36:309-27
    • (2001) Int. J. Numer. Methods Fluids , vol.36 , pp. 309-327
    • Lehoucq, R.B.1    Salinger, A.G.2
  • 91
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: A survey of approaches and applications
    • Knoll DA, Keyes DE. 2004. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193:357-97
    • (2004) J. Comput. Phys , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 92
    • 33751561755 scopus 로고    scopus 로고
    • Spatially distributed stochastic systems: Equation-free and equation-assisted bifurcation analysis
    • Qiao L, Erban R, Kelley CT, Kevrekidis IG. 2006. Spatially distributed stochastic systems: equation-free and equation-assisted bifurcation analysis. J. Chem. Phys. 125:204108
    • (2006) J. Chem. Phys , vol.125 , pp. 204108
    • Qiao, L.1    Erban, R.2    Kelley, C.T.3    Kevrekidis, I.G.4
  • 93
    • 0001435828 scopus 로고
    • On an iterative method for the solution of a system of finite-difference equations
    • D'Yakanov EG. 1961. On an iterative method for the solution of a system of finite-difference equations. Dokl. Akad. Nauk 138:522-25
    • (1961) Dokl. Akad. Nauk , vol.138 , pp. 522-525
    • D'Yakanov, E.G.1
  • 94
    • 0010999738 scopus 로고
    • The solution of elliptic difference equations by semiexplicit iterative techniques
    • Gunn JE. 1964. The solution of elliptic difference equations by semiexplicit iterative techniques. Numer. Math. 6:181-84
    • (1964) Numer. Math , vol.6 , pp. 181-184
    • Gunn, J.E.1
  • 95
    • 11944250211 scopus 로고    scopus 로고
    • Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators
    • Axelsson O, Karátson J. 2004. Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators. Numer. Math. 99:197-223
    • (2004) Numer. Math , vol.99 , pp. 197-223
    • Axelsson, O.1    Karátson, J.2
  • 96
    • 45149136816 scopus 로고
    • On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial-differential equations
    • Faber V, Manteuffel T, Parter S. 1990. On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial-differential equations. Adv. Appl. Math. 11:109-63
    • (1990) Adv. Appl. Math , vol.11 , pp. 109-163
    • Faber, V.1    Manteuffel, T.2    Parter, S.3
  • 97
    • 0027611137 scopus 로고
    • Optimal equivalent preconditioners
    • Manteuffel T, Otto J. 1993. Optimal equivalent preconditioners. SIAM J. Numer. Anal. 30:790-812
    • (1993) SIAM J. Numer. Anal , vol.30 , pp. 790-812
    • Manteuffel, T.1    Otto, J.2
  • 98
    • 67651126654 scopus 로고    scopus 로고
    • Equivalent operator preconditioning of equation-free Newton-Krylov computations
    • Manuscript submitted
    • Samaey G, Vanroose W, Kevrekidis IG. 2008. Equivalent operator preconditioning of equation-free Newton-Krylov computations. SIAM J. Numer. Anal. Manuscript submitted
    • (2008) SIAM J. Numer. Anal
    • Samaey, G.1    Vanroose, W.2    Kevrekidis, I.G.3
  • 99
    • 0041428215 scopus 로고    scopus 로고
    • Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum
    • Gear CW, Kevrekidis IG. 2003. Projective methods for stiff differential equations: problems with gaps in their eigenvalue spectrum. SIAM J. Sci. Comput. 24:1091-106
    • (2003) SIAM J. Sci. Comput , vol.24 , pp. 1091-1106
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 100
    • 9644276018 scopus 로고    scopus 로고
    • Analysis of the heterogeneous multiscale method for ordinary differential equations
    • EW
    • EW. 2003. Analysis of the heterogeneous multiscale method for ordinary differential equations. Commun. Math. Sci. 1:423-36
    • (2003) Commun. Math. Sci , vol.1 , pp. 423-436
  • 101
    • 27144438542 scopus 로고    scopus 로고
    • Heterogeneous multiscale methods for stiff ordinary differential equations
    • Engquist B, Tsai Y.-H. 2005. Heterogeneous multiscale methods for stiff ordinary differential equations. Math. Comput. 74:1707-42
    • (2005) Math. Comput , vol.74 , pp. 1707-1742
    • Engquist, B.1    Tsai, Y.-H.2
  • 102
    • 35548937006 scopus 로고    scopus 로고
    • Accuracy analysis of acceleration schemes for stiff multiscale problems
    • Vandekerckhove C, Roose D. 2008. Accuracy analysis of acceleration schemes for stiff multiscale problems. J. Comput. Appl. Math. 211:181-200
    • (2008) J. Comput. Appl. Math , vol.211 , pp. 181-200
    • Vandekerckhove, C.1    Roose, D.2
  • 103
    • 2442498534 scopus 로고    scopus 로고
    • Coarse projective kMC integration: Forward/reverse initial and boundary value problems
    • Rico-Martinez R, Gear CW, Kevrekidis IG. 2004. Coarse projective kMC integration: forward/reverse initial and boundary value problems. J. Comput. Phys. 196:474-89
    • (2004) J. Comput. Phys , vol.196 , pp. 474-489
    • Rico-Martinez, R.1    Gear, C.W.2    Kevrekidis, I.G.3
  • 104
    • 33846170062 scopus 로고    scopus 로고
    • Second-order accurate projective integrators for multiscale problems
    • Lee S, Gear CW. 2007. Second-order accurate projective integrators for multiscale problems. J. Comput. Appl. Math. 201:258-74
    • (2007) J. Comput. Appl. Math , vol.201 , pp. 258-274
    • Lee, S.1    Gear, C.W.2
  • 105
    • 0036447606 scopus 로고    scopus 로고
    • Fourth order Chebyshev methods with recurrence relation
    • Abdulle A. Jan 2002. Fourth order Chebyshev methods with recurrence relation. SIAM J. Sci. Comput. 23:2041-54
    • (2002) SIAM J. Sci. Comput , vol.23 , pp. 2041-2054
    • Jan, A.A.1
  • 106
    • 0037408148 scopus 로고    scopus 로고
    • Telescopic projective methods for parabolic differential equations
    • Gear CW, Kevrekidis IG. 2003. Telescopic projective methods for parabolic differential equations. J. Comput. Phys. 187:95-109
    • (2003) J. Comput. Phys , vol.187 , pp. 95-109
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 107
    • 0025243935 scopus 로고
    • Increasing the real stability boundary of explicit methods
    • Sommeijer BP. 1990. Increasing the real stability boundary of explicit methods. Comput. Math. Appl. 19:37-49
    • (1990) Comput. Math. Appl , vol.19 , pp. 37-49
    • Sommeijer, B.P.1
  • 108
    • 33846056966 scopus 로고    scopus 로고
    • Numerical stability analysis of an acceleration scheme for step size constrained time integrators
    • Vandekerckhove C, Roose D, Lust K. 2007. Numerical stability analysis of an acceleration scheme for step size constrained time integrators. J. Comput. Appl. Math. 200:761-77
    • (2007) J. Comput. Appl. Math , vol.200 , pp. 761-777
    • Vandekerckhove, C.1    Roose, D.2    Lust, K.3
  • 109
    • 24644448790 scopus 로고    scopus 로고
    • Samaey G, Roose D, Kevrekidis IG. 2005. The gap-tooth scheme for homogenization problems. SIAM Multiscale Model. Simul. 4:278-306
    • Samaey G, Roose D, Kevrekidis IG. 2005. The gap-tooth scheme for homogenization problems. SIAM Multiscale Model. Simul. 4:278-306
  • 110
    • 48249118227 scopus 로고    scopus 로고
    • Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators
    • Roberts AJ, Kevrekidis IG. 2005. Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators. ANZIAM J. 46:C637-57
    • (2005) ANZIAM J , vol.46
    • Roberts, A.J.1    Kevrekidis, I.G.2
  • 111
    • 85021663679 scopus 로고    scopus 로고
    • Li J, Kevrekidis Gear CW, Kevrekidis IG. 2003. Deciding the nature of the coarse equation through microscopic simulations: the baby-bathwater scheme. SIAM Multiscale Model. Simul. 1:391-407
    • Li J, Kevrekidis PG, Gear CW, Kevrekidis IG. 2003. Deciding the nature of the "coarse equation" through microscopic simulations: the baby-bathwater scheme. SIAM Multiscale Model. Simul. 1:391-407
  • 112
    • 31744447017 scopus 로고    scopus 로고
    • Patch dynamics with buffers for homogenization problems
    • Samaey G, Kevrekidis IG, Roose D. 2006. Patch dynamics with buffers for homogenization problems. J. Comput. Phys. 213:264-87
    • (2006) J. Comput. Phys , vol.213 , pp. 264-287
    • Samaey, G.1    Kevrekidis, I.G.2    Roose, D.3
  • 113
    • 3042718493 scopus 로고    scopus 로고
    • Projective integration methods for distributions
    • 2001-130, NEC Res. Inst, Princeton, N.J
    • Gear CW. 2001. Projective integration methods for distributions. Tech. Rep. TR 2001-130, NEC Res. Inst., Princeton, N.J.
    • (2001) Tech. Rep. TR
    • Gear, C.W.1
  • 114
    • 33644976427 scopus 로고    scopus 로고
    • An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
    • Erban R, Kevrekidis IG, Othmer H. 2006. An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal. Phys.DNonlinear Phenom. 215:1-24
    • (2006) Phys.DNonlinear Phenom , vol.215 , pp. 1-24
    • Erban, R.1    Kevrekidis, I.G.2    Othmer, H.3
  • 115
    • 0001623257 scopus 로고    scopus 로고
    • Hybrid atomistic-continuum formulations and the moving contact-line problem
    • Hadjiconstantinou NG. 1999. Hybrid atomistic-continuum formulations and the moving contact-line problem. J. Comput. Phys. 154:245-65
    • (1999) J. Comput. Phys , vol.154 , pp. 245-265
    • Hadjiconstantinou, N.G.1
  • 116
    • 84890200574 scopus 로고    scopus 로고
    • Finite difference patch dynamics for advection homogenization problems
    • ed. AN Gorban, N Kazantzis, IG Kevrekidis, HC Öttinger, C Theodoropoulos, pp, Berlin: Springer
    • Samaey G, Roose D, Kevrekidis IG. 2006. Finite difference patch dynamics for advection homogenization problems. In Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, ed. AN Gorban, N Kazantzis, IG Kevrekidis, HC Öttinger, C Theodoropoulos, pp. 205-24. Berlin: Springer
    • (2006) Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena , pp. 205-224
    • Samaey, G.1    Roose, D.2    Kevrekidis, I.G.3
  • 117
    • 0037232578 scopus 로고    scopus 로고
    • Aholistic finite difference approach models linear dynamics consistently
    • Roberts AJ. 2002. Aholistic finite difference approach models linear dynamics consistently. Math. Comput. 72:247-62
    • (2002) Math. Comput , vol.72 , pp. 247-262
    • Roberts, A.J.1
  • 118
    • 35748963495 scopus 로고    scopus 로고
    • General tooth boundary conditions for equation free modelling
    • Roberts AJ, Kevrekidis IG. 2007. General tooth boundary conditions for equation free modelling. SIAM J. Sci. Comput. 29:1495-510
    • (2007) SIAM J. Sci. Comput , vol.29 , pp. 1495-1510
    • Roberts, A.J.1    Kevrekidis, I.G.2
  • 121
    • 0033232023 scopus 로고    scopus 로고
    • Bubble flow simulations with the lattice Boltzmann method
    • Sankaranarayanan K, Shan X, Kevrekidis I. 1999. Bubble flow simulations with the lattice Boltzmann method. Chem. Eng. Sci. 54:4817-23
    • (1999) Chem. Eng. Sci , vol.54 , pp. 4817-4823
    • Sankaranarayanan, K.1    Shan, X.2    Kevrekidis, I.3
  • 122
    • 0002311168 scopus 로고    scopus 로고
    • Coarse bifurcation studies of bubble flow microscopic simulations
    • ed. N Markatos, I Yentekakis, A Karabelas, S Bebelis, S Boghosian, et al, pp, Athens: Cosmoware
    • Theodoropoulos C, Sankaranarayanan S, Sundaresan S, Kevrekidis IG. 2001. Coarse bifurcation studies of bubble flow microscopic simulations. In Proc. 3rd Pan-Hellenic Conf. Chem. Eng., ed. N Markatos, I Yentekakis, A Karabelas, S Bebelis, S Boghosian, et al., pp. 221-24. Athens: Cosmoware
    • (2001) Proc. 3rd Pan-Hellenic Conf. Chem. Eng , pp. 221-224
    • Theodoropoulos, C.1    Sankaranarayanan, S.2    Sundaresan, S.3    Kevrekidis, I.G.4
  • 124
    • 27144516347 scopus 로고    scopus 로고
    • Coarse nonlinear dynamics and metastability of fillingemptying transitions: Water in carbon nanotubes
    • Sriraman S, Kevrekidis IG, Hummer G. 2005. Coarse nonlinear dynamics and metastability of fillingemptying transitions: water in carbon nanotubes. Phys. Rev. Lett. 95:130603
    • (2005) Phys. Rev. Lett , vol.95 , pp. 130603
    • Sriraman, S.1    Kevrekidis, I.G.2    Hummer, G.3
  • 125
    • 17444389688 scopus 로고    scopus 로고
    • Coarse master equation from Bayesian analysis of replica molecular dynamics simulations
    • Sriraman S, Kevrekidis IG, Hummer G. 2005. Coarse master equation from Bayesian analysis of replica molecular dynamics simulations. J. Phys. Chem. B 109:6479-84
    • (2005) J. Phys. Chem. B , vol.109 , pp. 6479-6484
    • Sriraman, S.1    Kevrekidis, I.G.2    Hummer, G.3
  • 126
    • 0035829539 scopus 로고    scopus 로고
    • Water conduction through the hydrophobic channel of a carbon nanotube
    • Hummer G, Rasaiah J, Noworyta J. 2001. Water conduction through the hydrophobic channel of a carbon nanotube. Nature 144:188-90
    • (2001) Nature , vol.144 , pp. 188-190
    • Hummer, G.1    Rasaiah, J.2    Noworyta, J.3
  • 127
    • 11144344122 scopus 로고
    • Monte-Carlo simulation of model amphiphilic oil-water systems
    • Larson RG, Scriven LE, Davis HT. 1985. Monte-Carlo simulation of model amphiphilic oil-water systems. J. Chem. Phys. 83:2411-20
    • (1985) J. Chem. Phys , vol.83 , pp. 2411-2420
    • Larson, R.G.1    Scriven, L.E.2    Davis, H.T.3
  • 129
    • 19944391468 scopus 로고    scopus 로고
    • Coarse-grained kinetic computations for rare events: Application to micelle formation
    • Kopelevich D, Panagiotopoulos A, Kevrekidis I. 2005. Coarse-grained kinetic computations for rare events: application to micelle formation. J. Chem. Phys. 122:044908
    • (2005) J. Chem. Phys , vol.122 , pp. 044908
    • Kopelevich, D.1    Panagiotopoulos, A.2    Kevrekidis, I.3
  • 130
    • 1042300990 scopus 로고    scopus 로고
    • Computing in the past with forward integration
    • Gear CW, Kevrekidis IG. 2004. Computing in the past with forward integration. Phys. Lett.A 321:335-43
    • (2004) Phys. Lett.A , vol.321 , pp. 335-343
    • Gear, C.W.1    Kevrekidis, I.G.2
  • 131
    • 34548081500 scopus 로고    scopus 로고
    • An equation-free approach to analyzing heterogeneous cell population dynamics
    • Bold K, Zou Y, Kevrekidis I, Henson M. 2007. An equation-free approach to analyzing heterogeneous cell population dynamics. J. Math. Biol. 55:331-52
    • (2007) J. Math. Biol , vol.55 , pp. 331-352
    • Bold, K.1    Zou, Y.2    Kevrekidis, I.3    Henson, M.4
  • 132
    • 34047244894 scopus 로고    scopus 로고
    • Heterogeneous animal group models and their group-level alignment dynamics: An equation-free approach
    • Moon S, Nabet B, Leonard N, Levin S, Kevrekidis IG. 2007. Heterogeneous animal group models and their group-level alignment dynamics: an equation-free approach. J. Theor. Biol. 246:100-12
    • (2007) J. Theor. Biol , vol.246 , pp. 100-112
    • Moon, S.1    Nabet, B.2    Leonard, N.3    Levin, S.4    Kevrekidis, I.G.5
  • 133
    • 70449595331 scopus 로고    scopus 로고
    • Robust oscillations in SIS epidemics on adaptive networks: Coarse graining by automated moment closure
    • Gross T, Kevrekidis IG. 2008. Robust oscillations in SIS epidemics on adaptive networks: coarse graining by automated moment closure. Europhys. Lett. 82:38004
    • (2008) Europhys. Lett , vol.82 , pp. 38004
    • Gross, T.1    Kevrekidis, I.G.2
  • 134
    • 17144394892 scopus 로고    scopus 로고
    • Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models
    • Cisternas J, Gear CW, Levin S, Kevrekidis IG. 2004. Equation-free modeling of evolving diseases: coarse-grained computations with individual-based models. Proc. R. Soc. Ser. A 460:2761-79
    • (2004) Proc. R. Soc. Ser. A , vol.460 , pp. 2761-2779
    • Cisternas, J.1    Gear, C.W.2    Levin, S.3    Kevrekidis, I.G.4
  • 135
    • 38849208541 scopus 로고    scopus 로고
    • Coarse-grained dynamics of an activity bump in a neural field model
    • Laing C, Frewen T, Kevrekidis I. 2007. Coarse-grained dynamics of an activity bump in a neural field model. Nonlinearity 20:2127-46
    • (2007) Nonlinearity , vol.20 , pp. 2127-2146
    • Laing, C.1    Frewen, T.2    Kevrekidis, I.3
  • 136
    • 27144557962 scopus 로고    scopus 로고
    • Core collapse via coarse dynamic renormalization
    • Szell A, Merritt D, Kevrekidis I. 2005. Core collapse via coarse dynamic renormalization. Phys. Rev. Lett. 95:081102
    • (2005) Phys. Rev. Lett , vol.95 , pp. 081102
    • Szell, A.1    Merritt, D.2    Kevrekidis, I.3
  • 137
    • 34247367647 scopus 로고    scopus 로고
    • Variable-free exploration of stochastic models: A gene regulatory network example
    • Erban R, Frewen TA, Wang X, Elston TC, Coifman R, et al. 2007. Variable-free exploration of stochastic models: a gene regulatory network example. J. Chem. Phys. 126:155103
    • (2007) J. Chem. Phys , vol.126 , pp. 155103
    • Erban, R.1    Frewen, T.A.2    Wang, X.3    Elston, T.C.4    Coifman, R.5
  • 138
    • 34248562494 scopus 로고    scopus 로고
    • Coarse molecular-dynamics analysis of stress-induced structural transitions in crystals
    • Amat M, Kevrekidis I, Maroudas D. 2007. Coarse molecular-dynamics analysis of stress-induced structural transitions in crystals. Appl. Phys. Lett. 90:171910
    • (2007) Appl. Phys. Lett , vol.90 , pp. 171910
    • Amat, M.1    Kevrekidis, I.2    Maroudas, D.3
  • 139
    • 0038824886 scopus 로고    scopus 로고
    • Microscopic/stochastic timesteppers and coarse control: A kinetic Monte Carlo example
    • Siettos CI, Armaou A, Makeev AG, Kevrekidis IG. 2003. Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example. AIChE J. 49:1922-26
    • (2003) AIChE J , vol.49 , pp. 1922-1926
    • Siettos, C.I.1    Armaou, A.2    Makeev, A.G.3    Kevrekidis, I.G.4
  • 140
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum JB, de Silva V, Langford JC. 2000. A global geometric framework for nonlinear dimensionality reduction. Science 5500:2319-23
    • (2000) Science , vol.5500 , pp. 2319-2323
    • Tenenbaum, J.B.1    de Silva, V.2    Langford, J.C.3
  • 141
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • Belkin M, Niyogi P. 2003. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comp. 15:1373-96
    • (2003) Neural Comp , vol.15 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 143
    • 33745342032 scopus 로고    scopus 로고
    • Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
    • Nadler B, Lafon S, Coifman R, Kevrekidis IG. 2006. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Appl. Comput. Harmon. A 21:113-27
    • (2006) Appl. Comput. Harmon. A , vol.21 , pp. 113-127
    • Nadler, B.1    Lafon, S.2    Coifman, R.3    Kevrekidis, I.G.4
  • 144
    • 84864071145 scopus 로고    scopus 로고
    • Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators
    • ed, J Platt, pp, Cambridge, MA: MIT Press
    • Nadler B, Lafon S, Coifman R, Kevrekidis IG. 2006. Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators. In Advances in Neural Information Processing Systems 18, ed. YWeiss, B Schölkopf, J Platt, pp. 955-62. Cambridge, MA: MIT Press
    • (2006) Advances in Neural Information Processing Systems 18 , pp. 955-962
    • Nadler, B.1    Lafon, S.2    Coifman, R.3    Kevrekidis, I.G.4
  • 145
    • 2342652956 scopus 로고    scopus 로고
    • Theory of inexact Krylov subspace methods and applications to scientific computing
    • Simoncini V, Szyld DB. 2003. Theory of inexact Krylov subspace methods and applications to scientific computing. SIAM J. Sci. Comput. 25:454-77
    • (2003) SIAM J. Sci. Comput , vol.25 , pp. 454-477
    • Simoncini, V.1    Szyld, D.B.2
  • 146
    • 55349094347 scopus 로고    scopus 로고
    • Givon D, Kevrekidis IG. 2008. Multiscale integration schemes for jump-diffusion systems. SIAM Multiscale Model. Simul. 7:495-516
    • Givon D, Kevrekidis IG. 2008. Multiscale integration schemes for jump-diffusion systems. SIAM Multiscale Model. Simul. 7:495-516
  • 148
    • 0041967046 scopus 로고    scopus 로고
    • A revolution in optical manipulation
    • Grier DG. 2003. A revolution in optical manipulation. Nature 424:810-16
    • (2003) Nature , vol.424 , pp. 810-816
    • Grier, D.G.1
  • 150
    • 33750189710 scopus 로고    scopus 로고
    • Laboratory observation of quantum control level sets
    • Roslund J, Roth M, Rabitz H. 2006. Laboratory observation of quantum control level sets. Phys. Rev. A 74:043414
    • (2006) Phys. Rev. A , vol.74 , pp. 043414
    • Roslund, J.1    Roth, M.2    Rabitz, H.3


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