@TechReport{ it:2015-025,
author = {Fritjof Fagerlund and Fredrik Hellman and Axel
M{\aa}lqvist and Auli Niemi},
title = {Improved {M}onte {C}arlo Methods for Computing Failure
Probabilities of Porous Media Flow Systems},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2015},
number = {2015-025},
month = aug,
abstract = {We study improvements of standard and multilevel Monte
Carlo methods for point evaluation of the cumulative
distribution function (failure probability) applied to
porous media two-phase flow simulations with uncertain
permeability. In an injection scenario with sweep
efficiency of the injected phase as quantity of interest,
we seek the probability that this quantity of interest is
smaller than a critical value. In the sampling procedure,
we use computable error bounds on the sweep efficiency
functional to solve only a subset of all realizations to
highest accuracy by means of what we call selective
refinement. We quantify the performance gains possible by
using selective refinement in combination with both the
standard and multilevel Monte Carlo method. We also
identify issues in the process of practical implementation
of the methods. We conclude that significant savings (one
order of magnitude) in computational cost are possible for
failure probability estimation in a realistic setting using
the selective refinement technique, both in combination
with standard and multilevel Monte Carlo.}
}