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 \geq 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 of \ll 1 s. Therefore the puzzle of QPOs with frequencies larger than 600 Hz still stands .