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In this paper the authors investigate three modeling techniques to simulate the time-dependent HDI problem for BPM disks. It is found that the Taylor expansion homogenization is the most economical accurate method for all ranges of pattern heights while the averaging method is only reliable for small pattern heights. Then the Taylor expansion homogenization method is applied to investigate the slider's flying attitude on the BPM disk. For small pattern heights, the minimum flying height loss is almost a linear function of the pattern height and area ratio. The experimentally observed empirical relation is verified. For larger pattern heights, they need to consider nonlinearities. Next, the slider's transition between two different pattern types is also studied for both large and small circumferential wedges of the servo zone. It is found that the slider's spacing increases and decreases periodically during transitions. The pitch and roll also change periodically but the maximum change is very small. Moreover, the peak-peak value of the minimum flying height for the small servo zone is smaller than that for the larger servo zone. And for real disk this peak-peak value might be even smaller if the extent of the servo zone is smaller. Finally, the authors select two different pattern types which can produce the same minimum flying height for the slider's transition study. It shows that using the selected pattern types, the slider's flying attitude remains almost constant across the transitions.