1436 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 2, MARCH 2004 An Unconditionally Stable Higher Order ADI-FDTD Technique for the Dispersionless Analysis of Generalized 3-D EMC Structures Nikolaos V. Kantartzis, Theodoros T. Zygiridis, and Theodoros D. Tsiboukis, Senior Member, IEEE Abstract—An efficient higher order alternating-direction im- plicit (ADI) finite-difference time–domain (FDTD) method for the unconditionally stable analysis of curvilinear electromagnetic com- patibity (EMC) applications is presented in this paper. The novel algorithm launches a class of precise spatial/temporal nonstandard forms that drastically suppress the dispersion errors of the ordi- nary approach as time-step increases and mitigate its strong de- pendence on cell shape or mesh resolution. For arbitrary inter- face media distributions that do not follow the grid lines, a con- vergent transformation based on a rigorous extrapolating practice is introduced. Moreover, infinite domains are successfully treated by optimized higher order curvilinear PMLs. Hence, the proposed technique achieves notable accuracy far beyond the Courant limit, subdues the ADI error mechanisms, and offers serious savings, as verified by the solution of several complex EMC problems. Index Terms—Alternating-direction implicit finite-difference time–domain (ADI-FDTD) method, curvilinear lattices, higher order nonstandard schemes, numerical dispersion. I. INTRODUCTION T HE PROGRESSIVELY rising demands for detailed models of modern electromagnetic compatibility (EMC) systems entail design tools that optimally exploit computer resources. Among existing schemes, the finite-difference time–domain (FDTD) technique has an indisputable popularity [1]. Its key restraint, though, in the prior problems, where cells must be much smaller than the shortest wavelength, is the Courant criterion, which involves excessive iterations. Lately, an unconditionally stable rendition of the FDTD method has been developed via the alternating-direction implicit (ADI) process [2], [3]. By splitting each time-step into two parts, this approach removes the stability limit, allowing any possible choice for a certain simulation. However, effective studies [4]–[9] revealed that dispersion errors depend closely on grid resolution, while their values are critically increased as the temporal increment becomes larger. So, to retain a high accu- racy level [10]–[15], the technique’s maximum time interval should be confined. It is the purpose of this paper to introduce a three-dimensional (3-D) curvilinear ADI-FDTD methodology, founded on dually Manuscript received July 1, 2003. This work was supported in part by the Greek General Secretariat of Research and Technology under Grant 01ED27. The authors are with the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, GR-54124, Greece (e-mail: tsibukis@auth.gr). Digital Object Identifier 10.1109/TMAG.2004.825289 Fig. 1. Curvilinear dual-cell complex (bars denote quantities in the secondary lattice) and a skewed mesh with localized discontinuities. mapped tensor concepts, for the elimination of the above defects and the precise modeling of realistic EMC structures. Through a unified framework, the new scheme establishes general higher order (HO) nonstandard forms and conducts alternations along mixed coordinates. This yields the extensive decrease of disper- sion errors and the reliable use of time-steps significantly be- yond the Courant condition. For dissimilar media, whose inter- face does not coincide with any of the mesh axes, the formula- tion hosts a convergent extrapolation, while the entire procedure is further improved by HO perfectly matched layers (PMLs). Results regarding various EMC arrangements that would nor- mally require prolonged simulations indicate the benefits of the proposed technique, even for very coarse tessellations. II. HO DISPERSION-OPTIMIZED SCHEME When arbitrarily curved geometries are to be modeled by the common ADI-FDTD method, the choice of large time inter- vals leads to substantial dispersion errors that degrade its per- formance. Not to mention the discrepancies due to the partial imposition of continuity conditions at complex grids (Fig. 1). In fact, the above problems have been the chief motive for our discretization strategy. The algorithm evaluates all spatial and temporal derivatives via the parametric 3-D HO nonstandard concepts (1) (2) with are real numbers, , and is a variable of the system defined by its metrics. Also, 0018-9464/04$20.00 © 2004 IEEE