Discrete transparent boundary conditions for the numerical solution of Fresnel's equation (Q1805440)

The authors present a construction scheme of deriving transparent, i.e., reflection free boundary conditions for the numerical solution of Fresnel's equation. In contrast to previous methods, this paper follows a different line of thought. The method advocated here treats the discrete problem after discretization of the time-like variable, i.e., in a Rothe method, which leads to a sequence of coupled boundary value problems. The boundary conditions thus obtained appear to be of a nonlocal Cauchy type. Each kind of linear implicit discretization induces its own discrete transparent boundary conditions. Numerical examples from integrated optics are given to illustrate the efficiency of the method.