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Abstract
We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing. We focus on the monoenergetic 1D slab geometry problem, with isotropic scattering, where the crosssections are lognormal correlated random fields of possibly low regularity. The paper includes an outline of novel theoretical results on the convergence of the discrete scheme, in the cases of both spatially variable and random crosssections. We also describe the theory and practice of algorithms for quantifying the uncertainty of a functional of the scalar flux, using Monte Carlo and quasi Monte Carlo methods, and their multilevel variants. A hybrid iterative/direct solver for computing each realisation of the functional is also presented. Numerical experiments show the effectiveness of the hybrid solver and the gains that are possible through quasiMonte Carlo sampling and multilevel variance reduction. For the multilevel quasiMonte Carlo method, we observe gains in the computational ε cost of up to two orders of magnitude over the standard Monte Carlo method, and we explain this theoretically. Experiments on problems with up to several thousand stochastic dimensions are included.
Original language  English 

Title of host publication  Contemporary Computational Mathematics  A Celebration of the 80th Birthday of Ian Sloan 
Publisher  Springer International Publishing 
Pages  455481 
Number of pages  27 
ISBN (Electronic)  9783319724560 
ISBN (Print)  9783319724553 
DOIs  
Publication status  Epub ahead of print  23 May 2018 
ASJC Scopus subject areas
 Mathematics(all)
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Dive into the research topics of 'Modern Monte Carlo variants for uncertainty quantification in neutron transport'. Together they form a unique fingerprint.Projects
 2 Finished

Multiscale Modelling of Aerospace Composites
Butler, R. & Scheichl, R.
Engineering and Physical Sciences Research Council
6/01/14 → 5/02/18
Project: Research council

Multilevel Monte Carlo Methods for Elliptic Problems
Scheichl, R.
Engineering and Physical Sciences Research Council
1/07/11 → 30/06/14
Project: Research council