  We investigate the three-dimensional structure of the pulsar magnetosphere
through time-dependent numerical simulations of a magnetic dipole that is set
in rotation. We developed our own Eulerian finite difference time domain
numerical solver of force-free electrodynamics and implemented the technique of
non-reflecting and absorbing outer boundaries. This allows us to run our
simulations for many stellar rotations, and thus claim with confidence that we
have reached a steady state. A quasi-stationary corotating pattern is
established, in agreement with previous numerical solutions. We discuss the
prospects of our code for future high-resolution investigations of dissipation,
particle acceleration, and temporal variability.
