  Electromagnetic scattering in moving structures is a fundamental topic in
physics and engineering. Yet, no general numerical solution to related problems
has been reported to date. We introduce here a generalized FDTD scheme to
remedy this deficiency. That scheme is an extension of the FDTD standard Yee
cell and stencil that includes not only the usual, physical fields, but also
auxiliary, unphysical fields allowing a straightforward application of moving
boundary conditions. The proposed scheme is illustrated by four examples -- a
moving interface, a moving slab, a moving crystal and a moving gradient -- with
systematic validation against exact solutions.
