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2019 | OriginalPaper | Chapter

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

Authors : Robin Schmidt, Matthias Voigt, Michele Pisaroni, Fabio Nobile, Penelope Leyland, Jordi Pons-Prats, Gabriel Bugeda

Published in: Uncertainty Management for Robust Industrial Design in Aeronautics

Publisher: Springer International Publishing

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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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previous chapter Surrogates for Combustion Instabilities in Annular Combustors
next chapter Latin Hypercube Sampling-Based Monte Carlo Simulation: Extension of the Sample Size and Correlation Control
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Metadata
Title
General Introduction to Monte Carlo and Multi-level Monte Carlo Methods
Authors
Robin Schmidt
Matthias Voigt
Michele Pisaroni
Fabio Nobile
Penelope Leyland
Jordi Pons-Prats
Gabriel Bugeda
Copyright Year
2019
Book
Uncertainty Management for Robust Industrial Design in Aeronautics

Print ISBN: 978-3-319-77766-5

Electronic ISBN: 978-3-319-77767-2

Copyright Year: 2019

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

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