Adaptive sampling method in deep-penetration particle transport problem

Deep-penetration problem has been one of the difficult problems in shielding calculation with Monte Carlo method for several decades. In this paper, a kind of particle transport random walking system under the emission point as a sampling station is built. Then, an adaptive sampling scheme is derived for better solution with the achieved information. The main advantage of the adaptive scheme is to choose the most suitable sampling number from the emission point station to obtain the minimum value of the total cost in the process of the random walk. Further, the related importance sampling method is introduced. Its main principle is to define the importance function due to the particle state and to ensure the sampling number of the emission particle is proportional to the importance function. The numerical results show that the adaptive scheme under the emission point as a station could overcome the difficulty of underestimation of the result in some degree, and the adaptive importance sampling method gets satisfied results as well.