Residual Monte Carlo for the One-Dimensional Particle Transport Equation
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© 2016 Society for Industrial and Applied Mathematics. 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.
author list (cited authors)
Peterson, J. R., Morel, J. E., & Ragusa, J. C.