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Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

Abstract

We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.

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Acknowledgements

This research was supported by the Ministry of Science and Technology, Taiwan, under grant no. 105-2221-E-002-025-MY3 and by National Taiwan University under grant no. 103R891805 (The NTU Excellence in Research Program). We are grateful to the National Center for High-Performance Computing and National Taiwan University for providing the computational resources.

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Correspondence to Chuin-Shan Chen.

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Lee, CS., Chen, YY., Yu, CH. et al. Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations. Comput Mech 60, 23–37 (2017). https://doi.org/10.1007/s00466-017-1389-0

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Keywords

  • Absorbing boundary condition
  • Molecular dynamics simulation
  • Time-history kernel