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Volumn 40, Issue 7, 1999, Pages 3353-3371

Symplectic-energy-momentum preserving variational integrators

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EID: 0033243778     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532892     Document Type: Article
Times cited : (207)

References (28)
  • 1
    • 0032476963 scopus 로고    scopus 로고
    • Multisymplectic geometry, variational integrators, and nonlinear PDEs
    • J. E. Marsden, G. W. Patrick, and S. Shkoller, "Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs," Commun. Math. Phys. 199, 351-395 (1998).
    • (1998) Commun. Math. Phys. , vol.199 , pp. 351-395
    • Marsden, J.E.1    Patrick, G.W.2    Shkoller, S.3
  • 2
    • 45449123467 scopus 로고
    • Lie-Poisson integrators and Lie-Poisson Hamilton-Jacobi theory
    • Z. Ge and J. E. Marsden, "Lie-Poisson integrators and Lie-Poisson Hamilton-Jacobi theory," Phys. Lett. A 133, 134-139 (1988).
    • (1988) Phys. Lett. A , vol.133 , pp. 134-139
    • Ge, Z.1    Marsden, J.E.2
  • 3
    • 0002859047 scopus 로고
    • Integrable discrete-time systems and difference operators
    • A. P. Veselov, "Integrable discrete-time systems and difference operators." Funct. Anal. Appl. 22, 83-94 (1988).
    • (1988) Funct. Anal. Appl. , vol.22 , pp. 83-94
    • Veselov, A.P.1
  • 4
    • 0001189154 scopus 로고
    • Integrable lagrangian correspondences and the factorization of matrix polynomials
    • A. P. Veselov, "Integrable Lagrangian correspondences and the factorization of matrix polynomials," Funct. Anal. Appl. 25, 112-123 (1991).
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 112-123
    • Veselov, A.P.1
  • 5
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • J. Moser and A. P. Veselov, "Discrete versions of some classical integrable systems and factorization of matrix polynomials," Commun. Math. Phys. 139, 217-243 (1991).
    • (1991) Commun. Math. Phys. , vol.139 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 6
    • 0031210701 scopus 로고    scopus 로고
    • Mechanical integrators derived from a discrete variaional principle
    • J. M. Wendlandt and J. E. Marsden, "Mechanical integrators derived from a discrete variaional principle," Physica D 106, 223-246 (1997).
    • (1997) Physica D , vol.106 , pp. 223-246
    • Wendlandt, J.M.1    Marsden, J.E.2
  • 10
    • 34249830447 scopus 로고
    • The discrete energy momentum method. Conserving algorithms for nonlinear elastodynamics
    • J. C. Simo and N. Tarnow, "The discrete energy momentum method. Conserving algorithms for nonlinear elastodynamics," ZAMP 43, 757-792 (1992).
    • (1992) ZAMP , vol.43 , pp. 757-792
    • Simo, J.C.1    Tarnow, N.2
  • 11
    • 0026939543 scopus 로고
    • Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
    • J. C. Simo, N. Tarnow, and K. K. Wong, "Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics," Comput. Methods Appl. Mech. Eng. 100, 63-116 (1992).
    • (1992) Comput. Methods Appl. Mech. Eng. , vol.100 , pp. 63-116
    • Simo, J.C.1    Tarnow, N.2    Wong, K.K.3
  • 12
    • 0003014117 scopus 로고    scopus 로고
    • Time integration and discrete Hamiltonian systems
    • O. Gonzalez, "Time integration and discrete Hamiltonian systems," J. Nonlinear Sci. 6, 449-468 (1996).
    • (1996) J. Nonlinear Sci. , vol.6 , pp. 449-468
    • Gonzalez, O.1
  • 13
    • 0009207683 scopus 로고
    • Time-discretization of Hamiltonian systems
    • Y. Shibberu, "Time-discretization of Hamiltonian systems," Comput. Math. Appl. 28, 123-145 (1994).
    • (1994) Comput. Math. Appl. , vol.28 , pp. 123-145
    • Shibberu, Y.1
  • 14
    • 0030213441 scopus 로고    scopus 로고
    • The use of Hamilton's principle to derive time-advance algorithms for ordinary differential equations
    • H. R. Lewis and P. Kostelec, "The use of Hamilton's principle to derive time-advance algorithms for ordinary differential equations," Comput. Phys. Commun. 96, 129-151 (1996).
    • (1996) Comput. Phys. Commun. , vol.96 , pp. 129-151
    • Lewis, H.R.1    Kostelec, P.2
  • 15
    • 0001529171 scopus 로고
    • Difference equations and conservation laws
    • T. D. Lee, "Difference equations and conservation laws," J. Stat. Phys. 46, 843-860 (1937).
    • (1937) J. Stat. Phys. , vol.46 , pp. 843-860
    • Lee, T.D.1
  • 16
    • 0001451136 scopus 로고
    • A note on energy conservation and stability of nonlinear time-stepping algorithms
    • M. Ortiz, "A note on energy conservation and stability of nonlinear time-stepping algorithms," Comput. Struct. 24, 167-168 (1986).
    • (1986) Comput. Struct. , vol.24 , pp. 167-168
    • Ortiz, M.1
  • 17
    • 0027886658 scopus 로고
    • Assessment of energy-momentum and symplectic schemes for stiff dynamical systems
    • New Orleans. December
    • J. C. Simo and O. Gonzalez, "Assessment of energy-momentum and symplectic schemes for stiff dynamical systems," in Proceedings ASME Winter Annual Meeting, New Orleans. December 1993.
    • (1993) Proceedings ASME Winter Annual Meeting
    • Simo, J.C.1    Gonzalez, O.2
  • 19
    • 0026916661 scopus 로고
    • A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems
    • F. Armero and J. C. Simo, "A New Unconditionally Stable Fractional Step Method for Non-Linear Coupled Thermomechanical Problems," Int. J. Numer. Methods Eng. 35, 737-766 (1992).
    • (1992) Int. J. Numer. Methods Eng. , vol.35 , pp. 737-766
    • Armero, F.1    Simo, J.C.2
  • 20
    • 0027187966 scopus 로고
    • A-priori stability estimates and unconditionally stable product formula algorithms for non-linear coupled thermoplasticity
    • F. Armero and J. C. Simo, "A-Priori Stability Estimates and Unconditionally Stable Product Formula Algorithms for Non-Linear Coupled Thermoplasticity," Int. J. Plast. 9, 149-182 (1993).
    • (1993) Int. J. Plast. , vol.9 , pp. 149-182
    • Armero, F.1    Simo, J.C.2
  • 21
    • 0030115145 scopus 로고    scopus 로고
    • Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and navier-stokes equations
    • F. Armero and J. C. Simo, "Long-Term Dissipativity of Time-Stepping Algorithms for an Abstract Evolution Equation with Applications to the Incompressible MHD and Navier-Stokes Equations," Comput. Methods Appl. Mech. Eng. 131, 41-90 (1996).
    • (1996) Comput. Methods Appl. Mech. Eng. , vol.131 , pp. 41-90
    • Armero, F.1    Simo, J.C.2
  • 22
    • 85033950250 scopus 로고    scopus 로고
    • The variational formulation of viscoplastic constitutive updates
    • to appear
    • M. Ortiz and L. Stainier, "The Variational formulation of viscoplastic constitutive updates," Comput. Methods Appl. Mech. Eng. (to appear).
    • Comput. Methods Appl. Mech. Eng.
    • Ortiz, M.1    Stainier, L.2
  • 23
    • 0003643366 scopus 로고    scopus 로고
    • Mechanics and symmetry
    • 2nd ed. Springer-Verlag, New York
    • J. E. Marsden and T. S. Ratiu, Mechanics and Symmetry, Texts in Applied Mathematics, Vol. 17, 2nd ed. (Springer-Verlag, New York, 1999).
    • (1999) Texts in Applied Mathematics , vol.17
    • Marsden, J.E.1    Ratiu, T.S.2
  • 27
    • 0000732463 scopus 로고
    • A limited memory algorithm for bound constrained optimization
    • R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu, "A limited memory algorithm for bound constrained optimization," J. Sci. Comput. 16, 1190-1208 (1995).
    • (1995) J. Sci. Comput. , vol.16 , pp. 1190-1208
    • Byrd, R.H.1    Lu, P.2    Nocedal, J.3    Zhu, C.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.