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Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation

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  • Poëtte, Gaël

Abstract

In this paper, we consider the linear Boltzmann equation subject to uncertainties in the initial conditions and matter parameters (cross-sections/opacities). In order to solve the underlying uncertain systems, we rely on moment theory and the construction of hierarchical moment models in the framework of parametric polynomial approximations. Such model is commonly called a generalized Polynomial Chaos (gPC) reduced model. In this paper, we prove the spectral convergence of the hierarchy of reduced model parametered by P (polynomial order) obtained from the uncertain linear Boltzmann equation.

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  • Poëtte, Gaël, 2020. "Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 24-45.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:24-45
    DOI: 10.1016/j.matcom.2020.04.009
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    References listed on IDEAS

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    1. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
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