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Multilevel Monte Carlo methods for computing failure probability of porous media flow systems
13 references·2 citing·31 second hopsampled
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References

  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2011Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients490 cited
  • 2011Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients296 cited
  • 2013Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients196 cited
  • 2013Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods187 cited
  • 2013Monte Carlo and Quasi-Monte Carlo Methods177 cited
  • 2014A continuation multilevel Monte Carlo algorithm121 cited
  • 2009On irregular functionals of SDEs and the Euler scheme85 cited
  • 2015Multilevel Monte Carlo Approximation of Distribution Functions and Densities70 cited
  • 2015Optimization of mesh hierarchies in multilevel Monte Carlo samplers47 cited
  • 2016A Multilevel Monte Carlo Method for Computing Failure Probabilities46 cited
  • 2013Multilevel Monte Carlo Methods33 cited
  • 2016MOLNs: A Cloud Platform for Interactive, Reproducible, and Scalable Spatial Stochastic Computational Experiments in Systems Biology Using PyURDME29 cited

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  • 2020Multifidelity Cross-Entropy Estimation of Conditional Value-at-Risk for Risk-Averse Design Optimization

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6 cited
  • 2022Quantify uncertainty by estimating the probability density function of the output of interest using MLMC based Bayes method5 cited