Approximated nonreflective

The most commonly used BC methods can be classified into three main categories the exact nonreflective BC, the approximated nonreflective BC (also called the variational BC or VBC), and the damping region BC. In principle, exact nonreflective BCs can be obtained via numerical computation for crystalline systems under certain assumptions.One possible formulation of this type of BC is discussed below. However, exact BCs are not local in both space and time, meaning that information about all of the boundary atoms at all times is, in principle, necessary to compute them. Because the decay of the history dependence is rather slow, implementing such a BC scheme can be computationally very expensive. To reduce such a computational cost, E and co-workers introduced the VBC scheme. 

Thus, ABC approximated in the form of Eq. (12.19) can be efficiently applied for ensuring nonreflecting outlet boundaries for two-dimensional disturbances. Such disturbances leave the computational domain for a limited time interval Ac Clearly, at At < t, the approximation of Eq. (12.19) is satisfactory. 

The single-scattering approximation applied to the equivalent transport problem for analysis of coUimated illumination in the case of nonreflecting surfaces Eqs. (65) to (68). 

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