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

Shaoqiang Tang & Songsong Ji

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 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.

  • 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 = {Shaoqiang Tang and Songsong Ji}, 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 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.

}, 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 - Shaoqiang Tang & Songsong Ji 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 KW - matching boundary condition KW - atomic simulation AB -

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.

Shaoqiang Tang & Songsong Ji. (1970). 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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