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A new generalized local time-step scheme is introduced to improve the computational efficiency of the finite-volume time-domain (FVTD) method. The flexibility of unstructured FVTD meshes is fully exploited by avoiding the disadvantage of a single short time step in the entire mesh. The great potential of this scheme is fully revealed in the FVTD simulation of electromagnetic (EM) problems with both large and fine structures in close proximity. The scheme is based on an automatic partition of the computational domain in subdomains where local time steps of the type 2ℓ-1Δt(ℓ=1,2,3,...) can be applied without violating the stability condition. Interfaces between subdomains are reduced to a generic two-level system which requires a very limited number of time interpolations during the FVTD iteration, therefore resulting in a very simple and robust technique. The application of local time stepping to three-dimensional EM problems demonstrates a significant speed-up of the computation without compromising the accuracy of the results.