  A fully-automated pole-tip shape optimization tool, involving write head
geometry construction, meshing, micromagnetic simulation and evaluation, is
presented. Optimizations have been performed for three different writing
schemes (centered, staggered and shingled) for an underlying bit patterned
media with an areal density of 2.12 Tdots/in$^2$ . Optimizations were performed
for a single-phase media with 10 nm thickness and a mag spacing of 8 nm. From
the computed write field and its gradient and the minimum energy barrier during
writing for islands on the adjacent track, the overall write error rate is
computed. The overall write errors are 0.7, 0.08, and 2.8 x 10$^{-5}$ for
centered writing, staggered writing, and shingled writing.
