Reply to "Comment on 'Performance of Halbach magnet with finite coercivity'"

We reply to Dr. Xu's comment on our paper 'Performance of Halbach magnet arrays with finite coercivity' (JMMM 407 (2016), 369-376). Contrary to Dr. Xu's objections we show that the procedure employed by us correctly accounts for the shape effects of the magnet elements. We show that the partial differential equation for the magnetic vector potential, derived from the Maxwell equations, incorporates all shape effects. On the other hand, the local constitutive relations express a point-wise link between, e.g., magnetic field and magnetic flux density, and are as such independent of geometry. We confirm that the results of our computations are perfectly consistent with the constitutive relation which is assumed as starting point.