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A fundamental scheme is utilised to efficiently implement the frequency-dependent 3D locally one-dimensional FDTD method. The formulation is performed in matrix-operator-free forms in the right-hand sides of resultant equations. A modified procedure, in which implicit and explicit equations are alternately calculated, needs to retain only 10 field arrays, while the traditional explicit FDTD requires 12. Analysis of a gap plasmonic waveguide validates the presented 3D LOD-FDTD method.