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By R. T. Compton

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In conclusion, the (2, 4) DRP-FDTD method accomplishes a noteworthy reduction of dispersion errors leading to reliable, accurate as well as convergent numerical simulations and thus may be deemed a significant contribution in the advancement of conventional higher order time-domain modeling. 4 Design of Controllable Dispersion-Error Techniques This section deals with the construction of optimal higher order FDTD schemes with adjustable dispersion error. Rather than implementing the ordinary approaches, based on Taylor series expansion, the modified finite-difference operators are designed via alternative procedures that enhance the wideband capabilities of the resulting numerical techniques.

41). , the global error, as a function of the Δt/Δh number and computational time are, respectively, illustrated. It becomes apparent that the implicit higher order schemes outperform Yee’s technique, achieving fast convergence in terms of a reasonable CPU overhead. 3 One-Sided Difference Operators for Homogeneous Dielectric Boundaries Implementing a domain-decomposition concept, accurate one-sided difference operators [26] are combined with extrapolation/interpolation techniques to treat dielectric interfaces as boundary points between separate subdomains.

So, it is derived that s i = Wi P and p i = Ii P. For the discretization of the 2M jump conditions, the algorithm uses central finitedifference schemes at each mesh node to construct 2M × 2M algebraic equations. cls April 27, 2006 17:18 CONVENTIONAL HIGHER ORDER FDTD DIFFERENTIATION 31 with q 2, j , j = 1, 2, . . , 2M, the suitable differencing weights acquired through the fast method of [18]. 65) known values which are independent of field values. 41) for the time update. Extension to the 2-D TM case opts for the vector form of ∂Q/∂t = R ∂Q/∂ x + Z ∂Q/∂ y with Q = [Hx Hy Ez]T .

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