@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.}
}