메뉴 건너뛰기




Volumn 7, Issue 4, 2009, Pages 1525-1548

Model dynamics across multiple length and time scales on a spatial multigrid

Author keywords

Advection ; Diffusion; Hierarchy; Multigrid; Renormalization; Slow manifold

Indexed keywords

COARSER GRID; COMPLEX DYNAMICS; HIERARCHY; MODEL DYNAMICS; MULTIGRID; NUMERICAL SIMULATION; RENORMALIZATION; SLOW MANIFOLD; SPATIAL GRIDS; TIME-SCALE; TWO TIME SCALE;

EID: 67649532603     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/080712349     Document Type: Article
Times cited : (8)

References (43)
  • 2
    • 0011607426 scopus 로고
    • A stochastic version of the centre manifold theorem
    • P. BOXLER, A stochastic version of the centre manifold theorem, Probab. Theory Related Fields, 83 (1989), pp. 509-545.
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 509-545
    • BOXLER, P.1
  • 4
    • 67649493209 scopus 로고    scopus 로고
    • Methods of Systematic Upscaling
    • Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, available online at
    • A. BRANDT, Methods of Systematic Upscaling, technical report, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, 2006; available online at http://wisdomarchive.wisdom. weizmann.ac.il:81/archive/00000398/.
    • (2006) technical report
    • BRANDT, A.1
  • 7
    • 0042540192 scopus 로고    scopus 로고
    • On the low-dimensional modelling of Stratonovich stochastic differential equations
    • X. CHAO AND A. J. ROBERTS, On the low-dimensional modelling of Stratonovich stochastic differential equations, Phys. A, 225 (1996), pp. 62-80.
    • (1996) Phys. A , vol.225 , pp. 62-80
    • CHAO, X.1    ROBERTS, A.J.2
  • 10
    • 67649471475 scopus 로고    scopus 로고
    • J. DOLBOW, M. A. KHALEEL, AND J. MITCHELL, Multiscale Mathematics Initiative: A Road-map. Report from the 3rd DoE Workshop on Multis cale Mathematics, technical report, Department of Energy, USA, 2004; available online at http://www.sc.doe.gov/ascr/mics/ amr.
    • J. DOLBOW, M. A. KHALEEL, AND J. MITCHELL, Multiscale Mathematics Initiative: A Road-map. Report from the 3rd DoE Workshop on Multis cale Mathematics, technical report, Department of Energy, USA, 2004; available online at http://www.sc.doe.gov/ascr/mics/ amr.
  • 11
    • 34548578612 scopus 로고    scopus 로고
    • The Heterogeneous Multiscale Method: A Review
    • Princeton University, Princeton, NJ, available online at
    • W. E, B. ENGQUIST, X. LI, W. REN, AND E. VANDEN-EUNDEN, The Heterogeneous Multiscale Method: A Review, technical report, Princeton University, Princeton, NJ, 2004; available online at http://www.math.princeton.edu/multiscale/ review.pdf.
    • (2004) technical report
    • ENGQUIST, W.E.B.1    LI, X.2    REN, W.3    VANDEN-EUNDEN, E.4
  • 12
    • 0001669344 scopus 로고
    • Normal form reductions for time-periodically driven differential equations
    • C. ELPHICK, G. IOOSS, AND E. TIRAPEGUI, Normal form reductions for time-periodically driven differential equations, Phys. Lett. A, 120 (1987), pp. 459-463.
    • (1987) Phys. Lett. A , vol.120 , pp. 459-463
    • ELPHICK, C.1    IOOSS, G.2    TIRAPEGUI, E.3
  • 13
    • 0032206010 scopus 로고    scopus 로고
    • Space-time continuous analysis of waveform relaxation for the heat equation
    • M. J. GANDER AND A. M. STUART, Space-time continuous analysis of waveform relaxation for the heat equation, SIAM J. Sci. Comput., 19 (1998), pp. 2014-2031.
    • (1998) SIAM J. Sci. Comput , vol.19 , pp. 2014-2031
    • GANDER, M.J.1    STUART, A.M.2
  • 14
    • 4243331271 scopus 로고
    • Systematic elimination of fast variables in linear systems
    • U. GEIGENMULLER, U. M. TITULAER, AND B. U. FELDERHOF, Systematic elimination of fast variables in linear systems, Phys. A, 119 (1983), pp. 41-52.
    • (1983) Phys. A , vol.119 , pp. 41-52
    • GEIGENMULLER, U.1    TITULAER, U.M.2    FELDERHOF, B.U.3
  • 15
    • 0001351025 scopus 로고
    • Asymptotic theory of the Boltzmann equation
    • H. GRAD, Asymptotic theory of the Boltzmann equation, Phys. Fluids, 6 (1963), pp. 147-181.
    • (1963) Phys. Fluids , vol.6 , pp. 147-181
    • GRAD, H.1
  • 16
    • 33947239428 scopus 로고    scopus 로고
    • Space-time approximation with sparse grids
    • M. GRIEBEL, D. OELTZ, AND P. VASSILEVSKI, Space-time approximation with sparse grids, SIAM J. Sci. Comput., 28 (2006), pp. 701-727.
    • (2006) SIAM J. Sci. Comput , vol.28 , pp. 701-727
    • GRIEBEL, M.1    OELTZ, D.2    VASSILEVSKI, P.3
  • 18
    • 0000907687 scopus 로고    scopus 로고
    • Multigrid waveform relaxation on spatial finite element meshes: The continuous-time case
    • J. JANSSEN AND S. VANDEWALLE, Multigrid waveform relaxation on spatial finite element meshes: The continuous-time case, SIAM J. Numer. Anal., 33 (1996), pp. 456-474.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 456-474
    • JANSSEN, J.1    VANDEWALLE, S.2
  • 19
    • 3042720018 scopus 로고    scopus 로고
    • Equation-free: The computer-assisted analysis of complex, multiscale systems
    • I. G. KEVREKIDIS, C. W. GEAR, AND G. HUMMER, Equation-free: The computer-assisted analysis of complex, multiscale systems, A. I. Ch. E. Journal, 50 (2004), pp. 1346-1354.
    • (2004) A. I. Ch. E. Journal , vol.50 , pp. 1346-1354
    • KEVREKIDIS, I.G.1    GEAR, C.W.2    HUMMER, G.3
  • 20
    • 85128858890 scopus 로고    scopus 로고
    • Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system level tasks
    • I. G. KEVREKIDIS, C. W. GEAR, J. M. HYMAN, P. G. KEVREKIDIS, O. RUNBORG, AND K. THEODOROPOULOS, Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system level tasks, Comm. Math. Sci., 1 (2003), pp. 715-762.
    • (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, K.6
  • 22
    • 57249110723 scopus 로고    scopus 로고
    • Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretization
    • T. MACKENZIE AND A. J. ROBERTS, Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretization, SIAM J. Appl. Dyn. Syst., 5 (2006), pp. 365-402.
    • (2006) SIAM J. Appl. Dyn. Syst , vol.5 , pp. 365-402
    • MACKENZIE, T.1    ROBERTS, A.J.2
  • 24
    • 67649481275 scopus 로고    scopus 로고
    • NATIONAL PHYSICAL LABORATORY, Notes on Applied Science 16, 2nd ed, Her Majesty's Stationery Office, London
    • NATIONAL PHYSICAL LABORATORY, Modern Computing Methods, Notes on Applied Science 16, 2nd ed., Her Majesty's Stationery Office, London, 196 1.
    • Modern Computing Methods , pp. 196-201
  • 25
    • 67649507750 scopus 로고    scopus 로고
    • An Introduction to Multiscale Methods
    • University of Warwick and Imperial College London, available online at
    • G. A. PAVLIOTIS AND A. M. STUART, An Introduction to Multiscale Methods, technical report, University of Warwick and Imperial College London, 2006; available online at http://www. maths.warwick .ac.uk/̃stuart.
    • (2006) technical report
    • PAVLIOTIS, G.A.1    STUART, A.M.2
  • 27
    • 0002563770 scopus 로고
    • Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems
    • A. J. ROBERTS, Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems, J. Austral. Math. Soc. B, 31 (1989), pp. 48-75.
    • (1989) J. Austral. Math. Soc. B , vol.31 , pp. 48-75
    • ROBERTS, A.J.1
  • 28
    • 0031099492 scopus 로고    scopus 로고
    • Low-dimensional modelling of dynamics via computer algebra
    • A. J. ROBERTS, Low-dimensional modelling of dynamics via computer algebra, Comput. Phys. Comm., 100 (1997), pp. 215-230.
    • (1997) Comput. Phys. Comm , vol.100 , pp. 215-230
    • ROBERTS, A.J.1
  • 29
    • 0035341644 scopus 로고    scopus 로고
    • Holistic discretisation ensures fidelity to Burgers' equation, Appl. Numer
    • A. J. ROBERTS, Holistic discretisation ensures fidelity to Burgers' equation, Appl. Numer. Modelling, 37 (2001), pp. 371-396.
    • (2001) Modelling , vol.37 , pp. 371-396
    • ROBERTS, A.J.1
  • 30
    • 0035892847 scopus 로고    scopus 로고
    • Holistic projection of initial conditions onto a finite difference approximation
    • A. J. ROBERTS, Holistic projection of initial conditions onto a finite difference approximation, Comput. Phys. Comm., 142 (2001), pp. 316-321.
    • (2001) Comput. Phys. Comm , vol.142 , pp. 316-321
    • ROBERTS, A.J.1
  • 31
    • 33644545273 scopus 로고    scopus 로고
    • Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids
    • A. J. ROBERTS, Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids, ANZIAM J., 43 (2001), pp. E1-E36. http://anziamj.austms.org.au/ojs/ index.php/ANZIAMJ/article/view/ 465.
    • (2001) ANZIAM J , vol.43
    • ROBERTS, A.J.1
  • 32
    • 0037232578 scopus 로고    scopus 로고
    • A holistic finite difference approach models linear dynamics consistently
    • A. J. ROBERTS, A holistic finite difference approach models linear dynamics consistently,Math. Comput., 72 (2002), pp. 247-262.
    • (2002) Math. Comput , vol.72 , pp. 247-262
    • ROBERTS, A.J.1
  • 33
    • 67649463226 scopus 로고    scopus 로고
    • A. J. ROBERTS, A step towards holistic discretisation of stochastic partial differential equations, in Proceedings of the 11th Computational Tech niques and Applications Conference (CTAC-2003), J. Crawford and A. J. Roberts, eds., ANZIAM J., 45 (2003), pp. C1-C15;http://anziamj.austms. org.au/ojs/index.php/ANZIAMJ/article/view/869.
    • A. J. ROBERTS, A step towards holistic discretisation of stochastic partial differential equations, in Proceedings of the 11th Computational Tech niques and Applications Conference (CTAC-2003), J. Crawford and A. J. Roberts, eds., ANZIAM J., 45 (2003), pp. C1-C15;http://anziamj.austms. org.au/ojs/index.php/ANZIAMJ/article/view/869.
  • 34
    • 35748963494 scopus 로고    scopus 로고
    • Resolving the multitude of microscale interactions accurately models stochastic partial differential equations
    • A. J. ROBERTS, Resolving the multitude of microscale interactions accurately models stochastic partial differential equations, LMS J. Comput. Math. . 9 (2006), pp. 193-221.
    • (2006) LMS J. Comput. Math , vol.9 , pp. 193-221
    • ROBERTS, A.J.1
  • 35
    • 67649486910 scopus 로고    scopus 로고
    • A. J. ROBERTS, Computer Algebra Models Dynamics on a Multigrid across Multiple Length and Time Scales, technical report, University of Southern Queensland, Toowoomba, QLD, Australia, 2007; available online at http://eprints.usq.edu.au/3373.
    • A. J. ROBERTS, Computer Algebra Models Dynamics on a Multigrid across Multiple Length and Time Scales, technical report, University of Southern Queensland, Toowoomba, QLD, Australia, 2007; available online at http://eprints.usq.edu.au/3373.
  • 36
    • 84921328985 scopus 로고    scopus 로고
    • A. J. ROBERTS, Subgrid and interelement interactions affect discretisations of stochastically forced diffusion, in Proceedings of the 13th Biennial Computational Techniques and Applications Conference (CTAC-2006), W. Read, J. W. Larson, and A. J. Roberts, eds., ANZIAM J., 48 (2007), pp. C168-C187; http://anziamj.austms.org.au/ojs/index.php/ ANZIAMJ/article/view/36.
    • A. J. ROBERTS, Subgrid and interelement interactions affect discretisations of stochastically forced diffusion, in Proceedings of the 13th Biennial Computational Techniques and Applications Conference (CTAC-2006), W. Read, J. W. Larson, and A. J. Roberts, eds., ANZIAM J., 48 (2007), pp. C168-C187; http://anziamj.austms.org.au/ojs/index.php/ ANZIAMJ/article/view/36.
  • 37
    • 35748935082 scopus 로고    scopus 로고
    • Normal form transforms separate slow and fast modes in stochastic dynamical systems
    • A. J. ROBERTS, Normal form transforms separate slow and fast modes in stochastic dynamical systems, Phys. A, 387 (2008), pp. 12-38.
    • (2008) Phys. A , vol.387 , pp. 12-38
    • ROBERTS, A.J.1
  • 38
  • 40
    • 33745955547 scopus 로고    scopus 로고
    • Space-time multigrid method for molecular dynamics simulations
    • H. WAISMAN and J. FISH, Space-time multigrid method for molecular dynamics simulations, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 6542-6559.
    • (2006) Comput. Methods Appl. Mech. Engrg , vol.195 , pp. 6542-6559
    • WAISMAN, H.1    FISH, J.2
  • 41
    • 38349088090 scopus 로고    scopus 로고
    • A heterogeneous space-time full approximation storage multilevel method for molecular dynamics simulations
    • H. WAISMAN and J. FISH, A heterogeneous space-time full approximation storage multilevel method for molecular dynamics simulations, Internat. J. Numer. Methods Engrg., 73 (2008), pp. 407-426.
    • (2008) Internat. J. Numer. Methods Engrg , vol.73 , pp. 407-426
    • WAISMAN, H.1    FISH, J.2
  • 42
    • 0000422597 scopus 로고
    • Variational methods and applications to water waves
    • Roy.Soc.London Proc
    • G. B. WHITHAM, Variational methods and applications to water waves, Roy.Soc.London Proc. Ser. A, 299 (1967), pp. 6-25.
    • (1967) Ser. A , vol.299 , pp. 6-25
    • WHITHAM, G.B.1
  • 43
    • 67649475079 scopus 로고
    • Parallelizing across Time When Solving Time-Dependent Partial Differential Equations
    • Technical Report ORNL/TM-11963, Oak Ridge National Laboratory, Oak Ridge, TN
    • P. H. wORLEY, Parallelizing across Time When Solving Time-Dependent Partial Differential Equations, Technical Report ORNL/TM-11963, Oak Ridge National Laboratory, Oak Ridge, TN, 1991.
    • (1991)
    • wORLEY, P.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.