Efficient and Robust Design for Absorbing Boundary Conditions in Atomistic Computations

We propose an efficient and robust way to design absorbing boundary conditions in atomistic computations. An optimal discrete boundary condition is obtained by minimizing a functional of reflection coefficient integral over a range of wave numbers. The minimization is performed with respect to a set of wave numbers, at which transparent absorption is reached. Compared with the optimization with respect to the boundary condition coefficients suggested by E and Huang [Phys. Rev. Lett. 87 (2001) 133501], we reduce considerably the number of independent variables and the computing cost. We further demonstrate with numerical examples that both the optimization and the wave absorption are more robust in the proposed design.