An Auto-Importance Sampling Method for Deep Penetration Problems

For many traditional radiation shielding problems as well as medical and nuclear well-logging applications, it has long been recognized that the analog Monte Carlo is inefficient, which are known especially in deep penetration problems.This arises from the fact that the particles have little chance of contributing to the solution far from the source when using analog procedures.Numerous variance reduction techniques have grown up to overcome this inefficiency.However, there are still some limitations.A further difficulty lies in the potential for biased results due to the misuse of variance reduction techniques or the statistical convergence of Monte Carlo results.Responding to these difficulties, a new variance reduction technique called "auto-importance sampling method" is proposed in this paper.In the new method, the geometry space is divided into sub-spaces by fictitious surfaces.On the fictitious surfaces, fictitious particles are created according to the importance distribution automatically and then they are transported.The particles' number is increased on each fictitious surface.With this method, it is unnecessary to make pre-calculations to test different parameters for the variance reduction technique, or to make another calculation to get the importance distribution.Two examples are simulated with the new method.It can be seen that the new variance reduction technique is very easy to use and the computational efficiency achieved is very encouraging.