메뉴 건너뛰기




Volumn 32, Issue 4, 2010, Pages 2029-2046

Heterogeneous multiscale methods for mechanical systems with vibrations

Author keywords

Constrained systems; Heterogeneous multiscale methods; Mechanical systems; Oscillatory problems

Indexed keywords

EQUATIONS OF MOTION; EQUATIONS OF STATE; NUMERICAL METHODS; VIBRATIONS (MECHANICAL);

EID: 77955685590     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/080738556     Document Type: Article
Times cited : (28)

References (31)
  • 2
    • 63049099014 scopus 로고    scopus 로고
    • A multiscale method for highly oscillatory ordinary differential equations with resonance
    • G. Ariel, B. Engquist, and R. Tsai, A multiscale method for highly oscillatory ordinary differential equations with resonance, Math. Comput., 78 (2009), pp. 929-956.
    • (2009) Math. Comput. , vol.78 , pp. 929-956
    • Ariel, G.1    Engquist, B.2    Tsai, R.3
  • 6
    • 61849106124 scopus 로고    scopus 로고
    • Instabilities and inaccuracies in the integration of highly oscillatory problems
    • M. P. Calvo and J. M. Sanz-Serna, Instabilities and inaccuracies in the integration of highly oscillatory problems, SIAM J. Sci. Comput., 31 (2009), pp. 1653-1677.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 1653-1677
    • Calvo, M.P.1    Sanz-Serna, J.M.2
  • 8
    • 77955673014 scopus 로고    scopus 로고
    • Higher-order averaging, formal series and numerical integration I: B-series, Found
    • Ph. Chartier, A. Murua, and J. M. Sanz-Serna, Higher-order averaging, formal series and numerical integration I: B-series, Found. Comput. Math., submitted.
    • Comput. Math., Submitted
    • Chartier, Ph.1    Murua, A.2    Sanz-Serna, J.M.3
  • 9
    • 9644276018 scopus 로고    scopus 로고
    • Analysis of the heterogeneous multiscale method for ordinary differential equations
    • W. E, Analysis of the heterogeneous multiscale method for ordinary differential equations, Comm. Math. Sci., 1 (2003), pp. 423-436.
    • (2003) Comm. Math. Sci. , vol.1 , pp. 423-436
  • 11
    • 85128805678 scopus 로고    scopus 로고
    • The heterogeneous multiscale methods
    • W. E, and B. Engquist, The heterogeneous multiscale methods, Comm. Math. Sci., 1 (2003), pp. 87-132.
    • (2003) Comm. Math. Sci. , vol.1 , pp. 87-132
    • Engquist, B.1
  • 13
    • 27144438542 scopus 로고    scopus 로고
    • Heterogeneous multiscale methods for stiff ordinary differential equations
    • B. Engquist and R. Tsai, Heterogeneous multiscale methods for stiff ordinary differential equations, Math. Comp., 74 (2005), pp. 1707-1742.
    • (2005) Math. Comp. , vol.74 , pp. 1707-1742
    • Engquist, B.1    Tsai, R.2
  • 14
  • 17
    • 0000545837 scopus 로고    scopus 로고
    • Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
    • L. Jay, Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, SIAM J. Numer. Anal., 33 (1996), pp. 368-387.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 368-387
    • Jay, L.1
  • 18
    • 33846170062 scopus 로고    scopus 로고
    • Second-order accurate projective integrators for multiscale problems
    • S. L. Lee and C. W. Gear, Second-order accurate projective integrators for multiscale problems, J. Comput. Appl. Math., 201 (2007), pp. 258-274.
    • (2007) J. Comput. Appl. Math. , vol.201 , pp. 258-274
    • Lee, S.L.1    Gear, C.W.2
  • 20
    • 0001900679 scopus 로고    scopus 로고
    • Geometry and physics of averaging with applications
    • M. Levi, Geometry and physics of averaging with applications, Phys. D, 132 (1999), pp. 150-164.
    • (1999) Phys. D , vol.132 , pp. 150-164
    • Levi, M.1
  • 21
    • 34548490943 scopus 로고    scopus 로고
    • Deciding the nature of the coarse equation through microscopic simulations: The baby-bathwater scheme
    • J. Li, P. G. Kevrekidis, C. W. Gear, and I. G. Kevrekidis, Deciding the nature of the coarse equation through microscopic simulations: The baby-bathwater scheme, SIAM Rev., 49 (2007), pp. 469-487.
    • (2007) SIAM Rev. , vol.49 , pp. 469-487
    • Li, J.1    Kevrekidis, P.G.2    Gear, C.W.3    Kevrekidis, I.G.4
  • 22
    • 9444274106 scopus 로고    scopus 로고
    • Effective Hamiltonian and dynamic stability of the inverted pendulum
    • G. J. Mata and E. Pestana, Effective Hamiltonian and dynamic stability of the inverted pendulum, European J. Phys., 25 (2004), pp. 717-721.
    • (2004) European J. Phys. , vol.25 , pp. 717-721
    • Mata, G.J.1    Pestana, E.2
  • 23
    • 0012144123 scopus 로고
    • Stability of the inverted pendulum subjected to almost periodic and stochastic base motion-an application of the method of averaging
    • R. Mitchell, Stability of the inverted pendulum subjected to almost periodic and stochastic base motion-an application of the method of averaging, Internat. J. Non-Linear Mech., 7 (1972), pp. 101-123.
    • (1972) Internat. J. Non-Linear Mech. , vol.7 , pp. 101-123
    • Mitchell, R.1
  • 24
    • 49749115247 scopus 로고    scopus 로고
    • Mollified impulse methods for highly oscillatory differential equations
    • J. M. Sanz-Serna, Mollified impulse methods for highly oscillatory differential equations, SIAM J. Numer. Anal., 46 (2008), pp. 1040-1059.
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 1040-1059
    • Sanz-Serna, J.M.1
  • 25
    • 44049087242 scopus 로고    scopus 로고
    • Stabilizing with a hammer
    • J. M. Sanz-Serna, Stabilizing with a hammer, Stoch. Dyn., 8 (2008), pp. 45-57.
    • (2008) Stoch. Dyn. , vol.8 , pp. 45-57
    • Sanz-Serna, J.M.1
  • 26
    • 67651156235 scopus 로고    scopus 로고
    • Modulated Fourier expansions and heterogeneous multiscale methods
    • J. M. Sanz-Serna, Modulated Fourier expansions and heterogeneous multiscale methods, IMA J. Numer. Anal., 29 (2009), pp. 595-605.
    • (2009) IMA J. Numer. Anal. , vol.29 , pp. 595-605
    • Sanz-Serna, J.M.1
  • 28
    • 21444435011 scopus 로고    scopus 로고
    • On the stabilization of a parametrically driven inverted double pendulum
    • K. Schiele, On the stabilization of a parametrically driven inverted double pendulum, ZAMM Z. Angew. Math. Mech., 77 (1997), pp. 143-146. (Pubitemid 127778513)
    • (1997) ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik , vol.77 , Issue.2 , pp. 143-146
    • Schiele, K.1
  • 29
    • 84880280809 scopus 로고    scopus 로고
    • Multiple time scale numerical methods for the inverted pendulum problem
    • B. Engquist, P. Lötsdedt, and O. Runborg, eds., Springer, Berlin
    • R. Sharp, Y.-H. Tsai, and B. Engquist, Multiple time scale numerical methods for the inverted pendulum problem, in Multiscale Methods in Science and Engineering, Lect. Notes Comput. Sci. Eng. 44, B. Engquist, P. Lötsdedt, and O. Runborg, eds., Springer, Berlin, 2005, pp. 241-261.
    • (2005) Multiscale Methods in Science and Engineering, Lect. Notes Comput. Sci. Eng , vol.44 , pp. 241-261
    • Sharp, R.1    Tsai, Y.-H.2    Engquist, B.3
  • 30
    • 85128824735 scopus 로고    scopus 로고
    • Numerical techniques for multi-scale dynamical systems with multiple time scales
    • E. Vanden-Eijnden, Numerical techniques for multi-scale dynamical systems with multiple time scales, Comm. Math. Sci., 1 (2003), pp. 385-391.
    • (2003) Comm. Math. Sci. , vol.1 , pp. 385-391
    • Vanden-Eijnden, E.1
  • 31
    • 34547284818 scopus 로고    scopus 로고
    • On HMM-like integrators and projective integration methods for systems with multiple time scales
    • E. Vanden-Eijnden, On HMM-like integrators and projective integration methods for systems with multiple time scales, Comm. Math. Sci., 5 (2007), pp. 495-505.
    • (2007) Comm. Math. Sci. , vol.5 , pp. 495-505
    • Vanden-Eijnden, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.