descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 2012 English Publisher:Elsevier BVJournal:Computer Methods in Applied Mechanics and Engineering, volume 225-228, pages 116-127 (issn: 0045-7825,

Authors: Florentin, Eric; Díez, Pedro;

doi: 10.1016/j.cma.2012.03.016

handle: 2117/116664

Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems

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Abstract

In the framework of stochastic non-intrusive finite element modeling, a common practice is using Monte Carlo simulation. The main drawback of this approach is the computational cost, because it requires computing a large number of deterministic finite element solutions. The different Monte Carlo samplings correspond to realizations of the random variables characterizing the stochastic behavior of the model. Thus, this requires solving a set deterministic problems with the same structure, that is with variations concerning the material parameters and the loading data. Consequently, the different problems to be solved are in practice similar to each other. The reduced basis strategy is therefore a sensible option to reduce computational cost, provided that the quality of the numerical solution is guaranteed. The paper introduces a goal-oriented strategy allowing to successively enrich the reduced basis along the Monte Carlo process. The method is based on assessing the error of the reduced basis solution with a residual estimate for the prescribed quantity of interest. The efficiency of the proposed approach, which is particularly important if the number of independent random variables is large, is illustrated in 1D and 2D mechanical examples.

Peer Reviewed

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
French National Centre for Scientific Research
France
Universitat Politècnica de Catalunya
Spain
UniverSud Paris
France
University of Paris-Saclay
France

Keywords

:65 Numerical analysis::65G Error analysis and interval analysis [Classificació AMS], Engineering, Civil, Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant, Finite element methods applied to problems in solid mechanics, Anàlisi estocàstica, Engineering, Multidisciplinary, Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis, Stochastic modeling, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, reduced basis, Reduced basis, adaptivity, :Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC], Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis, goal-oriented error assessment, :60 Probability theory and stochastic processes::60H Stochastic analysis [Classificació AMS], :Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant [Àrees temàtiques de la UPC], Goal-oriented error assessment, Engineering, Ocean, Engineering, Aerospace, Engineering, Biomedical, Anàlisi numèrica, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, Random materials and composite materials, Monte Carlo methods, Stochastic analysis, Computer Science, Software Engineering, Engineering, Marine, Engineering, Manufacturing, Engineering, Mechanical, Adaptivity, Classical linear elasticity, Engineering, Industrial, stochastic modeling, Numerical analysis

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