No abstract

No abstract

No abstract

We propose an exact non-reflecting boundary condition for simulations of a square lattice in finite atomic sub-domain. The boundary condition is based on the series expansion of the single source kernel functions. The time history kernel Laplace transform is first derived in a closed form, where the Fourier transform inversion is performed analytically. An efficient numerical procedure is also developed for the inverse Laplace transform. Differences in the finite boundary condition and the infinite boundary approximation elucidate the cause of the long-lasting difficulty of corner effects. Numerical tests verify accuracy of the proposed approach.

We propose a class of efficient matching boundary conditions to suppress spurious reflection for multiscale computations of one dimensional diatomic chains. This provides the first local effective treatment of both acoustic and optical phonons. Adopting the extended zone scheme of the dispersion relation, we design a class of force boundary conditions by enforcing perfect absorption at certain selected wave numbers. Reflection suppression is improved by involving more neighboring atoms in the condition. The effectiveness of the proposed matching boundary conditions is demonstrated by reflection coefficient analysis, numerical tests, and comparisons with the time history treatment.