RESIDUAL MONTE CARLO FOR THE ONE-DIMENSIONAL PARTICLE TRANSPORT EQUATION

An exponentially convergent residual Monte Carlo method for the monoenergetic, slab-geometry, particle transport equation is defined and tested. The method is based upon the use of a linear-discontinuous finite-element space in position and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to maintain exponential convergence after stagnation occurs due to inadequate finite-element resolution. In addition, a biased sampling algorithm is used to adequately converge problems with high levels of local mesh refinement. Although the algorithm uses a finite-element space to represent the solution, one obtains the projection of the exact Monte Carlo solution onto the finite-element space. Computational results are presented demonstrating the efficacy of the new approach.