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A systematic higher-order FDTD-PML methodology for the accurate simulation of complex curvilinear 3-D EMC problems is presented in this paper. Developing an efficient covariant-contravariant vector classification, the novel technique introduces a parametric family of higher-order non-standard schemes for the suppression of the critical dispersion errors. The wider spatial stencils near boundary walls are treated by self-adaptive compact operators, while for the temporal variable a multi-stage leapfrog integration is utilized. Moreover, this optimal formulation leads to enhanced curvilinear PMLs that significantly annihilate outgoing waves. Numerical validation indicates the benefits of the proposed algorithm via several demanding and practical EMC applications.