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General Introduction to Monte Carlo and Multi-level Monte Carlo Methods

  • Robin SchmidtEmail author
  • Matthias Voigt
  • Michele Pisaroni
  • Fabio Nobile
  • Penelope Leyland
  • Jordi Pons-Prats
  • Gabriel Bugeda
Chapter
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 140)

Abstract

In this chapter, we present a general introduction to Monte Carlo (MC)-based methods, sampling methodologies, stratification methods, and variance reduction techniques. In the first part, we will discuss the theoretical basis and the convergence proprieties of MC methods. The next part is devoted to pseudorandom and quasi-random number generation, the generation of random variables and the application of stratification. It is followed by techniques for correlation and discrepancy control. The third part presents the concept of Latin Hypercube Sampling (LHS). The last part introduces the concept of Multi-Level Monte Carlo (MLMC).

Keywords

Monte Carlo Sampling Latin hypercube Variance reduction Multi-Level Monte Carlo 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Robin Schmidt
    • 1
    Email author
  • Matthias Voigt
    • 1
  • Michele Pisaroni
    • 2
  • Fabio Nobile
    • 2
  • Penelope Leyland
    • 2
  • Jordi Pons-Prats
    • 3
  • Gabriel Bugeda
    • 3
    • 4
  1. 1.Institute of Fluid MechanicsTechnische Universität DresdenDresdenGermany
  2. 2.Scientific Computing and Uncertainty QuantificationEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.CIMNE, Aeronautical GroupBarcelonaSpain
  4. 4.Universitat Politecnica de Catalunya - BarcelonaTechBarcelonaSpain

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