深穿透粒子输运问题的自适应抽样方法

屏蔽计算中的深穿透问题一直是蒙特卡罗计算的一个难题，研究了一种发射点作为驿站的随机游动机制，推导了相应的自适应抽样方法。其主要优势在于，在蒙特卡罗方法求解粒子输运的同时，利用已经获得的信息，自适应地控制各次抽样数，不断完善计算进程。通过对碰撞点引进重要性函数，实现发射点作为驿站的重要性抽样，并结合自适应控制达到最佳抽样状态。数值结果表明:基于发射点作为驿站的自适应抽样方法，在一定程度上克服了深穿透计算中估计值偏低现象。相应的重要函数抽样方法获得了满意的结果。

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.