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Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties


Abgrall, Rémi; Congedo, P. M; Geraci, G (2017). Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties. Mathematics and Computers in Simulation, 139:1-22.

Abstract

In the present work, a method for solving partial differential equations with uncertainties is presented. A multiresolution method, permitting to compute statistics for the entire solution and in presence of a whatever form of the probability density function, is extended to perform an adaptation in both physical and stochastic spaces. The efficiency of this strategy, in terms of refinement/coarsening capabilities, is demonstrated on several test-cases by comparing with respect to other more classical techniques, namely Monte Carlo (MC) and Polynomial Chaos (PC). Finally, the proposed strategy is applied to the heat equation showing very promising results in terms of accuracy, convergence and regularity.

Abstract

In the present work, a method for solving partial differential equations with uncertainties is presented. A multiresolution method, permitting to compute statistics for the entire solution and in presence of a whatever form of the probability density function, is extended to perform an adaptation in both physical and stochastic spaces. The efficiency of this strategy, in terms of refinement/coarsening capabilities, is demonstrated on several test-cases by comparing with respect to other more classical techniques, namely Monte Carlo (MC) and Polynomial Chaos (PC). Finally, the proposed strategy is applied to the heat equation showing very promising results in terms of accuracy, convergence and regularity.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:31 September 2017
Deposited On:24 Jan 2018 14:09
Last Modified:19 Aug 2018 10:32
Publisher:Elsevier
ISSN:0378-4754
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.matcom.2016.02.002
Project Information:
  • : FunderFP7
  • : Grant ID226316
  • : Project TitleADDECCO - Adaptive Schemes for Deterministic and Stochastic Flow Problems
  • : FunderFP7
  • : Grant ID226316
  • : Project TitleADDECCO - Adaptive Schemes for Deterministic and Stochastic Flow Problems

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