CONVERGENCE OF THE MONTE-CARLO ALGORITHMS FOR LINEAR TRANSPORT MODELING

We consider the convergency of the basic Monte Carlo (MC) algorithms f or solving the Boltzmann transport equation (BTE). It is a linear kine tic equation describing a broad class of particle transport phenomena such as electron and neutron transport, radiative transfer, medium ene rgy electron and ion scattering in solids, etc. The variety of the MC algorithms can be summarized in three main groups. The algorithms of t he first one simulate the natural chain of events, happening during th e physical process of the particle transport. The algorithms belonging to the other two generate the particle history back in time or modify the weight of the elementary events, thus achieving variance reductio n in desired regions of the phase space. It has been shown that all of them can be generated by the iteration approach (IA) - a method for o btaining MC algorithms by applying numerical MC techniques to the inte gral form of the BTE. The convergence proof is based on the IA and the convergence of the Neumann series of the integral form of the BTE. A discussion of the probable error is presented. (C) 1998 IMACS/Elsevier Science B.V.