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.
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