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Approximation of Probability Density Functions for PDEs with Random Parameters Using Truncated Series Expansions

Capodaglio, Giacomo, Gunzburger, Max and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2021) Approximation of Probability Density Functions for PDEs with Random Parameters Using Truncated Series Expansions. Vietnam Journal of Mathematics, 49 (3). pp. 685-711. ISSN 2305-221X

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Identification Number: 10.1007/s10013-020-00465-5

Abstract

The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two stochastic finite element methods, Monte Carlo sampling and the stochastic Galerkin method with global polynomials. The random variable is a functional of the solution of the random PDE, such as the average over the physical domain. The truncated series are obtained considering a finite number of terms in the Gram–Charlier or Edgeworth series expansions. These expansions approximate the PDF of a random variable in terms of another PDF, and involve coefficients that are functions of the known cumulants of the random variable. To the best of our knowledge, their use in the framework of PDEs with random parameters has not yet been explored.

Item Type: Article
Official URL: https://www.springer.com/journal/10013
Additional Information: © 2021 Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Date Deposited: 08 Feb 2024 12:27
Last Modified: 17 Apr 2024 04:12
URI: http://eprints.lse.ac.uk/id/eprint/121982

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