Generation of non-Gaussian vector-valued random fields for stochastic representation in multiscale analysis: an adaptive algorithm based on Itô stochastic differential equations

Abstract : This work is concerned with the construction of a novel random generator for non-Gaussian vector-valued random fields with values in non-polyhedral, bounded or semi-bounded subsets of Rn. Such an issue is of particular interest in the multiscale analysis and inverse identification of random heterogeneous materials, where the aforementionned random fields can be used as the stochastic coefficients of some elliptic partial differential operator (e.g. for the operator related to linear elasticity). The approach is based on two main ingredients. The first one is related to the theoretical construction of a family of auxiliary random fields converging, in some (stochastic) sense, towards the target random field. Each of these additional random fields is subsequently simulated by solving a family of Itô stochastic differential equations. The second ingredient is the definition of an adaptive algorithm that prevents the scheme from diverging (on the fly) whenever the current state of the diffusion at some point reaches the neighboorhood of the admissible set.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01061954
Contributor : J. Guilleminot <>
Submitted on : Monday, September 8, 2014 - 6:44:29 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:13 PM

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  • HAL Id : hal-01061954, version 1

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Johann Guilleminot, Christian Soize. Generation of non-Gaussian vector-valued random fields for stochastic representation in multiscale analysis: an adaptive algorithm based on Itô stochastic differential equations. 14th European Mechanics of Materials Conference 2014 (EMMC14), Aug 2014, Gothenburg, Sweden. pp.Pages: 1-1. ⟨hal-01061954⟩

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