Skip to main content
×
Home
    • Aa
    • Aa

Stability of Atomic Simulations with Matching Boundary Conditions

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

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.

Copyright
Corresponding author
Corresponding author. Email: maotang@pku.edu.cn
Email: songsong.0211@163.com
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 14 *
Loading metrics...

* Views captured on Cambridge Core between 9th April 2017 - 25th April 2017. This data will be updated every 24 hours.