Introducing PHAEDRA: a new spectral code for simulations of relativistic   magnetospheres
  We describe a new scheme for evolving the equations of force-free electrodynamics, the vanishing-inertia limit of magnetohydrodynamics. This pseudospectral code uses global orthogonal basis function expansions to take accurate spatial derivatives, allowing the use of an unstaggered mesh and the complete force-free current density. The method has low numerical dissipation and diffusion outside of singular current sheets. We present a range of one- and two-dimensional tests, and demonstrate convergence to both smooth and discontinuous analytic solutions. As a first application, we revisit the aligned rotator problem, obtaining a steady solution with resistivity localised in the equatorial current sheet outside the light cylinder. 
Kyle Parfrey, Andrei M. Beloborodov, and Lam Hui
astro-ph.HE physics.comp-ph