Maximum Accuracy and Optimized Compact Schemes

This robust higher order finite-difference method, originally presented in [10,13,25], develops a seven-point spatial operator along with an explicit six-stage time-advancing technique of the Runge-Kutta form. For the former operator, two central-difference suboperators are required a) an antisymmetric 

On the other hand, the temporal update of differential equation d 3j dt = f(u, t) is conducted in terms of 

Proceeding to the manipulation of interfaces that have dissimilar dielectric properties, each region is modeled as a separate domain and the outcomes are coupled via the pertinent continuity conditions. This idea enables the distinct generation of diverse grids with the desired resolution. More specifically, at the interface between two dielectric media or a perfect electric conducting (PEC) boundary, a local flux-vector formulation of Maxwell s equations is considered. Therefore, as discussed in [25] for incoming waves, derivatives are approximated by 

FIGURE2.2 Treatment of Ez components at a lattice terminated by a PEC boundary and an absorbing boundary condition 

Another effective means to confine the stencil size in the case of PEC boundaries are the central compact operators [5, 7], implemented for the higher order FDTD method in [14], and expressed as 

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