  The seismological dynamics of magnetars is largely determined by a strong
hydro-magnetic coupling between the solid crust and the fluid core. In this
paper we set up a "spectral" computational framework in which the magnetar's
motion is decomposed into a series of basis functions which are associated with
the crust and core vibrational eigenmodes. A general-relativistic formalism is
presented for evaluation of the core Alfven modes in the magnetic-flux
coordinates, as well for eigenmode computation of a strongly magnetized crust
of finite thickness. By considering coupling of the crustal modes to the
continuum of Alfven modes in the core, we construct a fully relativistic
dynamical model of the magnetar which allows: i) Fast and long simulations
without numerical dissipation. ii) Very fine sampling of the stellar structure.
We find that the presence of strong magnetic field in the crust results in
localizing of some high-frequency crustal elasto-magnetic modes with the radial
number n>1 to the regions of the crust where the field is nearly horizontal.
While the hydro-magnetic coupling of these localized modes to the Alfven
continuum in the core is reduced, their energy is drained on a time-scale much
less than 1 second. Therefore the puzzle of the observed QPOs with frequencies
larger than 600 Hz still stands.
