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Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields

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Abstract

We present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented.

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Acknowledgments

Part of this research was conducted while the second author was staying at École Centrale Paris as an Invited Professor. Both the authors would like to thank École Centrale Paris (CentraleSupélec) for this invitation.

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Authors and Affiliations

  1. Laboratoire MSSMat UMR 8579, CentraleSupélec, CNRS, Châtenay-Malabry, France

    R. Cottereau

  2. Laboratori de Càlcul Numèric, Departament de Matemàtica Aplicada III, International Center for Numerical Methods in Engineering (CIMNE), Universitat Politècnica de Catalunya, C/Jordi Girona 1-3, Campus Nord, Edifici C2, 08034, Barcelona, Spain

    P. Díez

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Cottereau, R., Díez, P. Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields. Comput Mech 56, 601–612 (2015). https://doi.org/10.1007/s00466-015-1190-x

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