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The systematic construction of a 3D generalized explicit method with adjustable mesh density is presented in this paper for the consistent analysis of large-scale applications. The novel algorithm introduces a parametric hybridization of a conformal multimodal finite-difference time-domain and a curvilinear pseudospectral time-domain technique which lead to optimized simulations. Updated independently, these procedures are interconnected by flexible boundary conditions and Runge-Kutta integrators, while their media sensitivity receives efficient tuning. Further enhancement is achieved via stencil patterns that exploit structural periodicity. So, the proposed schemes yield highly precise and affordable results devoid of grid errors, as certified by several real-world problems.