  Highly magnetized neutron stars are promising candidates to explain some of
the most peculiar astronomical phenomena, for instance, fast radio bursts,
gamma-ray bursts, and superluminous supernovae. Pulsations of these highly
magnetized neutron stars are also speculated to produce detectable
gravitational waves. In addition, pulsations are important probes of the
structure and equation of state of the neutron stars. The major challenge in
studying the pulsations of highly magnetized neutron stars is the demanding
numerical cost of consistently solving the nonlinear Einstein and Maxwell
equations under minimum assumptions. With the recent breakthroughs in numerical
solvers, we investigate pulsation modes of non-rotating neutron stars which
harbour strong purely toroidal magnetic fields of $10^{15-17}$ G through
two-dimensional axisymmetric general-relativistic magnetohydrodynamics
simulations. We show that stellar oscillations are insensitive to magnetization
effects until the magnetic to binding energy ratio goes beyond 10%, where the
pulsation mode frequencies are strongly suppressed. We further show that this
is the direct consequence of the decrease in stellar compactness when the
extreme magnetic fields introduce strong deformations of the neutron stars.
