  The GPU-accelerated track finding method is investigated to track electrons
from neutrinoless muon decay in the COMET Phase-I experiment. Inside the
cylindrical drift chamber, one third of the signal electron trajectories are
composed of multiple turns where the correct hit assignments to each turn
partition are significant in the track finding. Scanning all possible track
seeds of position and momentum can resolve the hit-to-turn assignment problem
with a high robustness, but requires a huge computational cost: The initial
track seeds $(\theta,z,p_x,p_y,p_z)$ have broad uncertainties, so there exists
many number of seeds that should be compared. In this article, this problem of
massive computations are mitigated with 1) the parallel computing of
Runge-Kutta-Nystr\"om track propagation with the GPU, and 2) an initial guess
on the seeds using the Hough transform and the detector geometry. The
computation speed enhancement compared to the CPU is also presented.
