Track finding with GPU-implemented fourth order Runge-Kutta (RK) method is investigated
to track electrons from muon decay in the COMET drift chamber. In the COMET
drift chamber, about 30-40 \% of signal events are composed of multiple turns where the right hit
assignments to each turn partition are significant in the track finding. Scanning all possible track seeds can resolve the hit-to-track assignment problem with a high robustness about the noise
hits, but requires a huge computational cost because of two reasons: 1) The adaptive RK method to
propagate the electron track needs small global errors, corresponding to small step sizes. 2) Initial
track seeds $(\theta, z, p_{x}, p_{y}, p_{z})$ have broad uncertainties, so many initial seeds should be tried and compared. In this presentation, these problems of massive
computations are mitigated with 1) the parallel computing of RK track propagation, which assigns
each track to each GPU block unit, 2) a better initial guess on the track
seeds using the Hough transform and the geometrical property of the cylindrical drift chamber.