Exponentially-convergent Monte Carlo for the 1-D transport equation Conference Paper uri icon


  • We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach.

author list (cited authors)

  • Peterson, J. R., Morel, J. E., & Ragusa, J. C.

publication date

  • September 2013