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Volume 29, Issue 2
Accurate Boundary Conditions for Twin Boundary

Shaoqiang Tang & Xi Zhu

DOI: 10.4208/cicp.OA-2019-0070

Commun. Comput. Phys., 29 (2021), pp. 399-419.

Published online: 2020-12

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  • Abstract

In this paper, we propose accurate numerical boundary conditions for atomic simulations of twin boundary. The heterogeneity of the lattice structure induces physical reflection across the twin boundary. When numerical boundary and the twin boundary coincide, the goal is to reproduce the correct amount of physical reflection. In particular, we consider waves periodic in the direction parallel to the twin boundary and reduce the problem into a complex-valued chain motion. Using Laplace transform, we design time history kernel (THK) treatment. We further design matching boundary conditions (MBC) by reproducing physical reflection at long wave limit and a specific wave number. Reflection analysis and numerical tests demonstrate the effectiveness of the proposed THK and MBC treatments.

  • Keywords

Twin boundary, artificial boundary condition, dispersion relation, reflection coefficient, atomic simulation.

  • AMS Subject Headings

74J05, 74M25, 37N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-399, author = {Tang , Shaoqiang and Zhu , Xi}, title = {Accurate Boundary Conditions for Twin Boundary}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {2}, pages = {399--419}, abstract = {

In this paper, we propose accurate numerical boundary conditions for atomic simulations of twin boundary. The heterogeneity of the lattice structure induces physical reflection across the twin boundary. When numerical boundary and the twin boundary coincide, the goal is to reproduce the correct amount of physical reflection. In particular, we consider waves periodic in the direction parallel to the twin boundary and reduce the problem into a complex-valued chain motion. Using Laplace transform, we design time history kernel (THK) treatment. We further design matching boundary conditions (MBC) by reproducing physical reflection at long wave limit and a specific wave number. Reflection analysis and numerical tests demonstrate the effectiveness of the proposed THK and MBC treatments.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0070}, url = {http://global-sci.org/intro/article_detail/cicp/18471.html} }
TY - JOUR T1 - Accurate Boundary Conditions for Twin Boundary AU - Tang , Shaoqiang AU - Zhu , Xi JO - Communications in Computational Physics VL - 2 SP - 399 EP - 419 PY - 2020 DA - 2020/12 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2019-0070 UR - https://global-sci.org/intro/article_detail/cicp/18471.html KW - Twin boundary, artificial boundary condition, dispersion relation, reflection coefficient, atomic simulation. AB -

In this paper, we propose accurate numerical boundary conditions for atomic simulations of twin boundary. The heterogeneity of the lattice structure induces physical reflection across the twin boundary. When numerical boundary and the twin boundary coincide, the goal is to reproduce the correct amount of physical reflection. In particular, we consider waves periodic in the direction parallel to the twin boundary and reduce the problem into a complex-valued chain motion. Using Laplace transform, we design time history kernel (THK) treatment. We further design matching boundary conditions (MBC) by reproducing physical reflection at long wave limit and a specific wave number. Reflection analysis and numerical tests demonstrate the effectiveness of the proposed THK and MBC treatments.

Tang , Shaoqiang and Zhu , Xi. (2020). Accurate Boundary Conditions for Twin Boundary. Communications in Computational Physics. 29 (2). 399-419. doi:10.4208/cicp.OA-2019-0070
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