FDTD method for piecewise homogeneous dielectric media

In this paper, we consider a numerical solution of Maxwell's curl equations for piecewise uniform dielectric medium by the example of a one-dimensional problem. For obtaining the second order accuracy, the electric field grid node is placed into the permittivity discontinuity point of the medium. If the dielectric permittivity is large, the problem becomes singularly perturbed and a contrast structure appears. We propose a piecewise quasi-uniform mesh which resolves all characteristic solution parts of the problem (regular part, boundary layer and transition zone placed between them) in detail. The features of the mesh are discussed.