  The radiofrequency dielectric response of the lead-free
Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ relaxor ferroelectric is simulated using a
coarse-grained Hamiltonian. This concept, taken from Real-Space Renormalization
Group theories, allows depicting the collective behavior of correlated local
modes gathered in blocks. Free-energy barriers for their thermally activated
collective hopping are deduced from this {\it ab-initio}-based approach, and
used as input data of Kinetic Monte Carlo simulations. The resulting numerical
scheme allows to simulate the dielectric response for external field
frequencies ranging from the kHz up to a few tens of MHz for the first time,
and to, e.g., demonstrate that local (electric or elastic) random fields lead
to the dielectric relaxation in the radiofrequency range that has been observed
in relaxors.
