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Stability of Atomic Simulations with Matching Boundary Conditions

  • Shaoqiang Tang (a1) and Songsong Ji (a1)

We explore the stability of matching boundary conditions in one space dimension, which were proposed recently for atomic simulations (Wang and Tang, Int. J. Numer. Mech. Eng., 93 (2013), pp. 1255-1285). For a finite segment of the linear harmonic chain, we construct explicit energy functionals that decay along with time. For a nonlinear atomic chain with its nonlinearity vanished around the boundaries, an energy functional is constructed for the first order matching boundary condition. Numerical verifications are also presented.

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[1] S. A. Adelman and J. D. Doll , Generalized Langevin equation appraochfor atom/solid-surface scattering: collinear atom/harmonic chain model, J. Chem. Phys., 61 (1974), pp. 42424245.

[2] W. Cai , M. De Koning , V. V. Bulatov and S. Yip , Minimizing boundary reflections in coupled-domain simulations, Phys. Rev. Lett., 85 (2000), pp. 32133216.

[3] M. Dreher AND S. Tang , Time history interfacial conditions in multiscale computations of lattice oscillations, Comput. Mech., 41 (2008), pp. 683698.

[5] M. Fang , S. Tang , Z. Li and X. Wang , Artificial boundary conditions for atomic simulations of face-centered-cubic lattice, Comput. Mech., 50 (2012), pp. 645655.

[8] W. K. Liu , E. G Karpov AND H. S. Park , Nano-Mechanics and Materials: Theory, Multiscale Methods and Applications, Wiley, 2005.

[9] G. Pang AND S. Tang , Time history kernel junctions for square lattice, Comput. Mech., 48 (2011), pp. 699711.

[10] S. Savadatti and M. Guddati , Absorbing boundary conditions for scalar waves in anisotropic media, part 1: time harmonic modeling, J. Comput. Phys., 229 (2010), pp. 66966714.

[11] S. Tang , A finite difference approach with velocity interfacial conditions for multiscale computations of crystalline solids, J. Comput. Phys., 227 (2008), pp. 40384062.

[13] S. Tang , T. Y. Hou and W. K. Liu , A mathematical framework of the bridging scale method, Int. J. Numer. Methods Eng., 65 (2006), pp. 16881713.

[14] 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. 5785.

[15] L. N. Trefethen , Stability of finite-difference models containing two boundaries or interfaces, Math. Comput., 45 (1985), pp. 279300.

[16] A. To AND S. Li , Perfectly matched multiscale simulations, Phys. Rev. B, 72 (2005), 035414.

[17] G. J. Wagner AND W. k. Liu , Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys., 190 (2003), pp. 249274.

[18] X. Wang and S. Tang , Matching boundary conditions for lattice dynamics, Int. J. Numer. Methods Eng., 93 (2013), pp. 12551285.

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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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