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

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Uncertainty Management for Robust Industrial Design in Aeronautics

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((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).

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Author information

Authors and Affiliations

  1. Institute of Fluid Mechanics, Technische Universität Dresden, 01062, Dresden, Germany

    Robin Schmidt & Matthias Voigt

  2. Scientific Computing and Uncertainty Quantification, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Michele Pisaroni, Fabio Nobile & Penelope Leyland

  3. CIMNE, Aeronautical Group, 08034, Barcelona, Spain

    Jordi Pons-Prats & Gabriel Bugeda

  4. Universitat Politecnica de Catalunya - BarcelonaTech, 08034, Barcelona, Spain

    Gabriel Bugeda

Authors
  1. Robin Schmidt
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  2. Matthias Voigt
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  3. Michele Pisaroni
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  4. Fabio Nobile
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  5. Penelope Leyland
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  6. Jordi Pons-Prats
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  7. Gabriel Bugeda
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Corresponding author

Correspondence to Robin Schmidt .

Editor information

Editors and Affiliations

  1. NUMECA International S.A., Brussels, Belgium

    Charles Hirsch

  2. NUMECA International S.A., Brussels, Belgium

    Dirk Wunsch

  3. Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw, Poland

    Jacek Szumbarski

  4. Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw, Poland

    Łukasz Łaniewski-Wołłk

  5. CIMNE International Centre for Numerical Methods in Engineering, Barcelona, Spain

    Jordi Pons-Prats

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Schmidt, R. et al. (2019). General Introduction to Monte Carlo and Multi-level Monte Carlo Methods. In: Hirsch, C., Wunsch, D., Szumbarski, J., Łaniewski-Wołłk, Ł., Pons-Prats, J. (eds) Uncertainty Management for Robust Industrial Design in Aeronautics . Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-319-77767-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-77767-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77766-5

  • Online ISBN: 978-3-319-77767-2

  • eBook Packages: EngineeringEngineering (R0)

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