Skip to main content
×
×
Home

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
References
Hide All
[1]Adelman S. A. and Doll J. D., Generalized Langevin equation appraochfor atom/solid-surface scattering: collinear atom/harmonic chain model, J. Chem. Phys., 61 (1974), pp. 42424245.
[2]Cai W., De Koning M., Bulatov V. V. and Yip S., Minimizing boundary reflections in coupled-domain simulations, Phys. Rev. Lett., 85 (2000), pp. 32133216.
[3]Dreher M. AND Tang S., Time history interfacial conditions in multiscale computations of lattice oscillations, Comput. Mech., 41 (2008), pp. 683698.
[4]Fang M., Boundary Treatments and Statistical Convergence of Particle Simulations, PhD Thesis, Peking University, Beijing, 2012.
[5]Fang M., Tang S., Li Z. and Wang X., Artificial boundary conditions for atomic simulations of face-centered-cubic lattice, Comput. Mech., 50 (2012), pp. 645655.
[6]Fang M., Wang X., Li Z. and Tang S., Matching boundary conditions for scalar waves in face-centered-cubic lattice, Adv. Appl. Math. Mech., 5 (2013), pp. 337350.
[7]Karpov E. G., Park H. S., Liu W. K. and Dorofeev D. L., On the modelling of chaotic thermal motion in solids, Preprint.
[8]Liu W. K., Karpov E. G AND Park H. S., Nano-Mechanics and Materials: Theory, Multiscale Methods and Applications, Wiley, 2005.
[9]Pang G. AND Tang S., Time history kernel junctions for square lattice, Comput. Mech., 48 (2011), pp. 699711.
[10]Savadatti S. and Guddati M., Absorbing boundary conditions for scalar waves in anisotropic media, part 1: time harmonic modeling, J. Comput. Phys., 229 (2010), pp. 66966714.
[11]Tang S., A finite difference approach with velocity interfacial conditions for multiscale computations of crystalline solids, J. Comput. Phys., 227 (2008), pp. 40384062.
[12]Tang S. and Fang M., Unstable surface modes infinite chain computations: deficiency of reflection coefficient approach, Commun. Comput. Phys., 8 (2010), pp. 143158.
[13]Tang S., Hou T. Y. and Liu W. K., A mathematical framework of the bridging scale method, Int. J. Numer. Methods Eng., 65 (2006), pp. 16881713.
[14]Tang S., Hou T. Y. and Liu w. k., A pseudo-spectral multiscale method: interfacial conditions and coarse grid equations, J. Comput. Phys., 213 (2006), pp. 5785.
[15]Trefethen L. N., Stability of finite-difference models containing two boundaries or interfaces, Math. Comput., 45 (1985), pp. 279300.
[16]To A. AND Li S., Perfectly matched multiscale simulations, Phys. Rev. B, 72 (2005), 035414.
[17]Wagner G. J. AND Liu W. k., Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys., 190 (2003), pp. 249274.
[18]Wang X. and Tang S., Matching boundary conditions for lattice dynamics, Int. J. Numer. Methods Eng., 93 (2013), pp. 12551285.
[19]Yong W. and Zhu Y., Convergence of finite difference method for nonlinear movable boundary problem, Science in China, Series A, 8 (1989), pp. 785795 (in Chinese).
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: 13 *
Loading metrics...

Abstract views

Total abstract views: 78 *
Loading metrics...

* Views captured on Cambridge Core between 9th April 2017 - 22nd January 2018. This data will be updated every 24 hours.