메뉴 건너뛰기




Volumn 7, Issue 1, 2008, Pages 294-320

The discontinuous galerkin method for the multiscale modeling of dynamics of crystalline solids

Author keywords

Discontinuous Galerkin method, multiscale model; Dynamics of crystalline solids; Molecular dynamics

Indexed keywords

ATOMIC SCALES; ATOMISTIC MODELS; CELL-BASED; CONTINUUM DESCRIPTIONS; CRYSTALLINE SOLIDS; DISCONTINUOUS GALERKIN METHOD, MULTISCALE MODEL; DISCONTINUOUS GALERKIN METHODS; DISPLACEMENT FIELDS; ELASTO DYNAMICS; FREE SPACES; GOVERNING EQUATIONS; MULTISCALE MODELING; MULTISCALE MODELS; NUMERICAL SIMULATIONS;

EID: 55249111832     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/070701212     Document Type: Article
Times cited : (11)

References (50)
  • 1
    • 33645900290 scopus 로고    scopus 로고
    • A space-time discontinuous Galerkin method for linearized elastodynamics with element-wise momentum balance
    • R. ABEDI, B. PETRACOVICI, and R. B. HABER, A space-time discontinuous Galerkin method for linearized elastodynamics with element-wise momentum balance, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 3247-3273.
    • (2006) Comput. Methods Appl. Mech. Engrg , vol.195 , pp. 3247-3273
    • ABEDI, R.1    PETRACOVICI, B.2    HABER, R.B.3
  • 2
    • 0032534356 scopus 로고    scopus 로고
    • Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture
    • F. F. ABRAHAM, J. Q. BROUGHTON, N. BERNSTEIN, and E. KAXIRAS, Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture, Europhys. Lett., 44 (1998), pp. 783-787.
    • (1998) Europhys. Lett , vol.44 , pp. 783-787
    • ABRAHAM, F.F.1    BROUGHTON, J.Q.2    BERNSTEIN, N.3    KAXIRAS, E.4
  • 3
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • D. N. ARNOLD, F. BREZZI, B. COCKBURN, and L. D. MARINI, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2002), pp. 1749-1779.
    • (2002) SIAM J. Numer. Anal , vol.39 , pp. 1749-1779
    • ARNOLD, D.N.1    BREZZI, F.2    COCKBURN, B.3    MARINI, L.D.4
  • 5
    • 0038109871 scopus 로고    scopus 로고
    • Stability of perfectly matched layers, group velocities and anisotropic waves
    • E. BÈCACHE, S. FAUQUEUX, and P. JOLY, Stability of perfectly matched layers, group velocities and anisotropic waves, J. Comput. Phys., 188 (2003), pp. 399-433.
    • (2003) J. Comput. Phys , vol.188 , pp. 399-433
    • BÈCACHE, E.1    FAUQUEUX, S.2    JOLY, P.3
  • 6
    • 28044459877 scopus 로고
    • A perfectly matched layer for the absorption of electromagnetic waves
    • J. P. BÈRENGER, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), pp. 185-200.
    • (1994) J. Comput. Phys , vol.114 , pp. 185-200
    • BÈRENGER, J.P.1
  • 7
    • 0000344261 scopus 로고
    • A general pressure tensor calculation for molecular dynamics simulations
    • D. BROWN and S. NEYERTZ, A general pressure tensor calculation for molecular dynamics simulations, Mol. Phys., 84 (1995), pp. 577-595.
    • (1995) Mol. Phys , vol.84 , pp. 577-595
    • BROWN, D.1    NEYERTZ, S.2
  • 8
    • 0037461642 scopus 로고    scopus 로고
    • Nonequilibrium molecular dynamics calculation of the thermal conductivity of solid materials
    • H. J. CASTEJON, Nonequilibrium molecular dynamics calculation of the thermal conductivity of solid materials, J. Phys. Chem. B, 107 (2003), pp. 826-828.
    • (2003) J. Phys. Chem. B , vol.107 , pp. 826-828
    • CASTEJON, H.J.1
  • 9
    • 34547596872 scopus 로고    scopus 로고
    • A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations
    • S. CHEN, W. E, Y.-X. LIU, and C.-W. SHU, A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations, J. Comput. Phys., 225 (2007), pp. 1314-1330.
    • (2007) J. Comput. Phys , vol.225 , pp. 1314-1330
    • CHEN, S.1    LIU, W.E.Y.-X.2    SHU, C.-W.3
  • 10
    • 0002718851 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for convection-dominated problems
    • Notes Comput. Sci. Eng. 9, T. J. Barth and H. Deconinck, eds, Springer, Berlin
    • B. COCKBURN, Discontinuous Galerkin methods for convection-dominated problems, in High- Order Methods for Computational Physics, Lect. Notes Comput. Sci. Eng. 9, T. J. Barth and H. Deconinck, eds., Springer, Berlin, 1999, pp. 69-224.
    • (1999) High- Order Methods for Computational Physics, Lect , pp. 69-224
    • COCKBURN, B.1
  • 12
    • 1442306605 scopus 로고    scopus 로고
    • Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
    • B. COCKBURN, F. LI, and C.-W. SHU, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, J. Comput. Phys., 194 (2004), pp. 588-610.
    • (2004) J. Comput. Phys , vol.194 , pp. 588-610
    • COCKBURN, B.1    LI, F.2    SHU, C.-W.3
  • 13
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems
    • B. COCKBURN, S.-Y. LIN, and C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems, J. Comput. Phys., 84 (1989), pp. 90-113.
    • (1989) J. Comput. Phys , vol.84 , pp. 90-113
    • COCKBURN, B.1    LIN, S.-Y.2    SHU, C.-W.3
  • 14
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework
    • B. COCKBURN and C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework, Math. Comp., 52 (1989), pp. 411-435.
    • (1989) Math. Comp , vol.52 , pp. 411-435
    • COCKBURN, B.1    SHU, C.-W.2
  • 15
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • B. COCKBURN and C.-W. SHU, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal., 35 (1998), pp. 2440-2463.
    • (1998) SIAM J. Numer. Anal , vol.35 , pp. 2440-2463
    • COCKBURN, B.1    SHU, C.-W.2
  • 16
    • 0001690553 scopus 로고    scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws V: Multidimensional systems
    • B. COCKBURN and C.-W. SHU, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws V: Multidimensional systems, J. Comput. Phys., 141 (1998), pp. 199-224.
    • (1998) J. Comput. Phys , vol.141 , pp. 199-224
    • COCKBURN, B.1    SHU, C.-W.2
  • 17
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convectiondominated problems
    • B. COCKBURN and C.-W. SHU, Runge-Kutta discontinuous Galerkin methods for convectiondominated problems, J. Sci. Comput., 16 (2001), pp. 173-261.
    • (2001) J. Sci. Comput , vol.16 , pp. 173-261
    • COCKBURN, B.1    SHU, C.-W.2
  • 18
    • 0035071437 scopus 로고    scopus 로고
    • Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media
    • F. COLLINO and C. TSOGKA, Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, 66 (2001), pp. 294-307.
    • (2001) Geophysics , vol.66 , pp. 294-307
    • COLLINO, F.1    TSOGKA, C.2
  • 19
    • 14944369585 scopus 로고    scopus 로고
    • Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics
    • F. COSTANZO and H. HUANG, Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 2059-2076.
    • (2005) Comput. Methods Appl. Mech. Engrg , vol.194 , pp. 2059-2076
    • COSTANZO, F.1    HUANG, H.2
  • 21
    • 4244079381 scopus 로고
    • Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals
    • M. S. DAW and M. I. BASKES, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B (3), 29 (1984), pp. 6443-6453.
    • (1984) Phys. Rev. B , vol.29 , Issue.3 , pp. 6443-6453
    • DAW, M.S.1    BASKES, M.I.2
  • 22
    • 33749330771 scopus 로고    scopus 로고
    • An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - II. The three-dimensional isotropic case
    • M. DUMBSER and M. KÄSER, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - II. The three-dimensional isotropic case, Geophys. J. Int., 167 (2006), pp. 319-336.
    • (2006) Geophys. J. Int , vol.167 , pp. 319-336
    • DUMBSER, M.1    KÄSER, M.2
  • 23
    • 85128805678 scopus 로고    scopus 로고
    • The heterogeneous multiscale methods
    • W. E and B. ENGQUIST, The heterogeneous multiscale methods, Commun. Math. Sci., 1 (2003), pp. 87-132.
    • (2003) Commun. Math. Sci , vol.1 , pp. 87-132
    • WEINAN, E.1    ENGQUIST, B.2
  • 26
    • 0001538909 scopus 로고
    • Canonical dynamics: Equilibrium phase-space distributions
    • W. G. HOOVER, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A (3), 31 (1985), pp. 1695-1697.
    • (1985) Phys. Rev. A , vol.31 , Issue.3 , pp. 1695-1697
    • HOOVER, W.G.1
  • 27
    • 0037045085 scopus 로고    scopus 로고
    • On the use of space-time finite elements in the solution of elastodynamic problems with strain discontinuities
    • H. HUANG and F. COSTANZO, On the use of space-time finite elements in the solution of elastodynamic problems with strain discontinuities, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 5315-5343.
    • (2002) Comput. Methods Appl. Mech. Engrg , vol.191 , pp. 5315-5343
    • HUANG, H.1    COSTANZO, F.2
  • 28
    • 0023960856 scopus 로고
    • Space-time finite element methods for elastodynamics: Formulations and error estimates
    • T. J. R. HUGHES and G. M. HULBERT, Space-time finite element methods for elastodynamics: Formulations and error estimates, Comput. Methods Appl. Mech. Engrg., 66 (1988), pp. 339-363.
    • (1988) Comput. Methods Appl. Mech. Engrg , vol.66 , pp. 339-363
    • HUGHES, T.J.R.1    HULBERT, G.M.2
  • 29
    • 33646967528 scopus 로고
    • The statistical mechanical theory of transport processes IV
    • J. H. IRVING and J. G. KIRKWOOD, The statistical mechanical theory of transport processes IV, J. Chem. Phys., 18 (1950), pp. 817-829.
    • (1950) J. Chem. Phys , vol.18 , pp. 817-829
    • IRVING, J.H.1    KIRKWOOD, J.G.2
  • 30
    • 33746173683 scopus 로고    scopus 로고
    • An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms
    • M. KÄSER and M. DUMBSER, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms, Geophys. J. Int., 166 (2006), pp. 855-877.
    • (2006) Geophys. J. Int , vol.166 , pp. 855-877
    • KÄSER, M.1    DUMBSER, M.2
  • 31
    • 38349049355 scopus 로고    scopus 로고
    • A space-time discontinuous Galerkin finite element method for fully coupled linear thermo-elasto-dynamic problems with strain and heat flux discontinuities
    • D. K. KHALMANOVA and F. COSTANZO, A space-time discontinuous Galerkin finite element method for fully coupled linear thermo-elasto-dynamic problems with strain and heat flux discontinuities, Comput. Methods Appl. Mech. Engrg., 197 (2008), pp. 1323-1342.
    • (2008) Comput. Methods Appl. Mech. Engrg , vol.197 , pp. 1323-1342
    • KHALMANOVA, D.K.1    COSTANZO, F.2
  • 32
    • 0035451516 scopus 로고    scopus 로고
    • An analysis of the quasicontinuum method
    • J. KNAP and M. ORTIZ, An analysis of the quasicontinuum method, J. Mech. Phys. Solids, 49 (2001), pp. 1899-1923.
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 1899-1923
    • KNAP, J.1    ORTIZ, M.2
  • 35
    • 25144454444 scopus 로고    scopus 로고
    • Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations
    • F. LI and C.-W. SHU, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations, Appl. Math. Lett., 18 (2005), pp. 1204-1209.
    • (2005) Appl. Math. Lett , vol.18 , pp. 1204-1209
    • LI, F.1    SHU, C.-W.2
  • 36
    • 18544383450 scopus 로고    scopus 로고
    • Multiscale modeling for dynamics of solids at finite temperature
    • X. LI and W. E, Multiscale modeling for dynamics of solids at finite temperature, J. Mech. Phys. Solids, 53 (2005), pp. 1650-1685.
    • (2005) J. Mech. Phys. Solids , vol.53 , pp. 1650-1685
    • LI, X.1    WEINAN, E.2
  • 37
    • 38849164239 scopus 로고    scopus 로고
    • Variational boundary conditions for molecular dynamics simulations of solids at low temperature
    • X. LI and W. E, Variational boundary conditions for molecular dynamics simulations of solids at low temperature, Commun. Comput. Phys., 1 (2006), pp. 135-175.
    • (2006) Commun. Comput. Phys , vol.1 , pp. 135-175
    • LI, X.1    WEINAN, E.2
  • 38
    • 34748861433 scopus 로고    scopus 로고
    • Boundary conditions for molecular dynamics simulations of solids: Treatment of the heat bath
    • X. LI and W. E, Boundary conditions for molecular dynamics simulations of solids: Treatment of the heat bath, Phys. Rev. B (3), 76 (2007), 104107.
    • (2007) Phys. Rev. B , vol.76 , Issue.3 , pp. 104107
    • LI, X.1    WEINAN, E.2
  • 39
    • 28144455569 scopus 로고
    • Nonoscillatory central differencing for hyperbolic conservation laws
    • H. NESSYAHU and E. TADMOR, Nonoscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
    • (1990) J. Comput. Phys , vol.87 , pp. 408-463
    • NESSYAHU, H.1    TADMOR, E.2
  • 40
    • 34547809547 scopus 로고
    • A unified formulation of the constant temperature molecular dynamics method
    • S. NOSÉ, A unified formulation of the constant temperature molecular dynamics method, J. Chem. Phys., 81 (1984), pp. 511-519.
    • (1984) J. Chem. Phys , vol.81 , pp. 511-519
    • NOSÉ, S.1
  • 42
    • 0041414829 scopus 로고    scopus 로고
    • Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity
    • B. RIVIÈRE, S. SHAW, M. F. WHEELER, and J. R. WHITEMAN, Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity, Numer. Math., 95 (2003), pp. 347-376.
    • (2003) Numer. Math , vol.95 , pp. 347-376
    • RIVIÈRE, B.1    SHAW, S.2    WHEELER, M.F.3    WHITEMAN, J.R.4
  • 43
    • 84966251037 scopus 로고
    • uniformly high-order schemes for conservation laws
    • C.-W. SHU, TVB uniformly high-order schemes for conservation laws, Math. Comp., 49 (1987), pp. 105-121.
    • (1987) Math. Comp , vol.49 , pp. 105-121
    • SHU, C.-W.1    TVB2
  • 44
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shockcapturing schemes
    • C.-W. SHU and S. OSHER, Efficient implementation of essentially non-oscillatory shockcapturing schemes, J. Comput. Phys., 77 (1988), pp. 439-471.
    • (1988) J. Comput. Phys , vol.77 , pp. 439-471
    • SHU, C.-W.1    OSHER, S.2
  • 45
    • 0030158774 scopus 로고    scopus 로고
    • Quasicontinuum analysis of defects in crystals
    • E. B. TADMOR, M. ORTIZ, and R. PHILLIPS, Quasicontinuum analysis of defects in crystals, Philos. Mag. A, 73 (1996), pp. 1529-1564.
    • (1996) Philos. Mag. A , vol.73 , pp. 1529-1564
    • TADMOR, E.B.1    ORTIZ, M.2    PHILLIPS, R.3
  • 46
    • 31744438879 scopus 로고    scopus 로고
    • A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations
    • S. TANG, T. Y. HOU, and W. K. LIU, A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations, J. Comput. Phys., 213 (2006), pp. 57-85.
    • (2006) J. Comput. Phys , vol.213 , pp. 57-85
    • TANG, S.1    HOU, T.Y.2    LIU, W.K.3
  • 47
    • 0000726819 scopus 로고
    • New empirical model for the structural properties of silicon
    • J. TERSOFF, New empirical model for the structural properties of silicon, Phys. Rev. Lett., 56 (1986), pp. 632-635.
    • (1986) Phys. Rev. Lett , vol.56 , pp. 632-635
    • TERSOFF, J.1
  • 48
    • 0042858270 scopus 로고    scopus 로고
    • Coupling of atomistic and continuum simulations using a bridging scale decomposition
    • G. J. WAGNER and W. K. LIU, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys., 190 (2003), pp. 249-274.
    • (2003) J. Comput. Phys , vol.190 , pp. 249-274
    • WAGNER, G.J.1    LIU, W.K.2
  • 49
    • 1842686579 scopus 로고    scopus 로고
    • A bridging domain method for coupling continua with molecular dynamics
    • S. P. XIAO and T. BELYTSCHKO, A bridging domain method for coupling continua with molecular dynamics, Comput. Methods Appl. Mech. Engrg., 193 (2004), pp. 1645-1669.
    • (2004) Comput. Methods Appl. Mech. Engrg , vol.193 , pp. 1645-1669
    • XIAO, S.P.1    BELYTSCHKO, T.2
  • 50
    • 0038693389 scopus 로고    scopus 로고
    • A local discontinuous Galerkin method for KdV type equations
    • J. YAN and C.-W. SHU, A local discontinuous Galerkin method for KdV type equations, SIAM J. Numer. Anal., 40 (2002), pp. 769-791.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 769-791
    • YAN, J.1    SHU, C.-W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.