RESIDUAL MONTE CARLO FOR THE ONE-DIMENSIONAL PARTICLE TRANSPORT EQUATION Academic Article

abstract

• 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.

authors

• Morel, Jim
• Ragusa, Jean

published proceedings

• SIAM JOURNAL ON SCIENTIFIC COMPUTING

author list (cited authors)

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

citation count

• 3

complete list of authors

• Peterson, JR||Morel, JE||Ragusa, JC

publication date

• January 2016

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Scientific Computing  Journal

keywords

• Adaptivity
• Exponential Convergence
• Monte Carlo

Digital Object Identifier (DOI)

• 10.1137/16M1057619

start page

• B941

end page

• B961

volume

• 38

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1137%2F16m1057619