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2024 | OriginalPaper | Chapter

Quasi Continuous Level Monte Carlo for Random Elliptic PDEs

Authors : Cedric Aaron Beschle, Andrea Barth

Published in: Monte Carlo and Quasi-Monte Carlo Methods

Publisher: Springer International Publishing

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Abstract

This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which therefore heavily influences the computational complexity. We propose in this paper a variant of the algorithm, where the exponentially distributed random variable is generated by a quasi Monte Carlo sequence, resulting in a significant variance reduction. In the examples presented the quasi continuous level Monte Carlo algorithm outperforms multilevel and continuous level Monte Carlo by a clear margin.

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Title: Quasi Continuous Level Monte Carlo for Random Elliptic PDEs
Authors: Cedric Aaron Beschle
Andrea Barth
Publisher: Springer International Publishing
Book: Monte Carlo and Quasi-Monte Carlo Methods
Print ISBN: 978-3-031-59761-9

Electronic ISBN: 978-3-031-59762-6

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-59762-6_1

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