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An efficient higher order alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method for the unconditionally stable analysis of curvilinear electromagnetic compatibility (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 ordinary approach as time-step increases and mitigate its strong dependence on cell shape or mesh resolution. For arbitrary interface media distributions that do not follow the grid lines, a convergent 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.