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Volume 6, Issue 5
Stability of Atomic Simulations with Matching Boundary Conditions

Shaoqiang Tang & Songsong Ji

DOI: 10.4208/aamm.2013.m360

Adv. Appl. Math. Mech., 6 (2014), pp. 539-551.

Published online: 2014-06

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  • Abstract

We explore the stability of matching boundary conditions in one space dimension, which was 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.

  • Keywords

Stability, matching boundary condition, atomic simulation.

  • AMS Subject Headings

70-08, 65L99, 34B60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-539, author = {Tang , Shaoqiang and Ji , Songsong}, title = {Stability of Atomic Simulations with Matching Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {5}, pages = {539--551}, abstract = {

We explore the stability of matching boundary conditions in one space dimension, which was 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m360}, url = {http://global-sci.org/intro/article_detail/aamm/34.html} }
TY - JOUR T1 - Stability of Atomic Simulations with Matching Boundary Conditions AU - Tang , Shaoqiang AU - Ji , Songsong JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 539 EP - 551 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m360 UR - https://global-sci.org/intro/article_detail/aamm/34.html KW - Stability, matching boundary condition, atomic simulation. AB -

We explore the stability of matching boundary conditions in one space dimension, which was 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.

Tang , Shaoqiang and Ji , Songsong. (2014). Stability of Atomic Simulations with Matching Boundary Conditions. Advances in Applied Mathematics and Mechanics. 6 (5). 539-551. doi:10.4208/aamm.2013.m360
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