  We present a two-timescale Floquet method that allows one to apply the
Kramers-Henneberger approach to short pulses and arbitrary laser frequencies.
An efficient numerical procedure to propagate the Floquet Hamiltonian is
provided that relies on the Toeplitz matrix formalism and Fast Fourier
Transformations. It enables efficient time propagation with large Floquet
expansions, while still taking advantage of the cycle-averaged
Kramers-Henneberger basis. Three illustrative cases of ionization with
different photon energies are analyzed, where the envelope of a short and
intense pulse is crucial to the underlying dynamics.
