Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods

Autor: Daniele Antonio Di Pietro, Olivier Le Maitre, Michele Botti, Pierre Sochala
Přispěvatelé: Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Politecnico di Milano [Milan] (POLIMI), Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Discretization
Computational Mechanics
General Physics and Astronomy
010103 numerical & computational mathematics
01 natural sciences
poroelasticity
Polynomial Chaos expansions
Pseudo-Spectral Projection methods
Convergence (routing)
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Applied mathematics
Mathematics - Numerical Analysis
0101 mathematics
Uncertainty quantification
Hybrid High-Order methods
Mathematics
Polynomial chaos
Mechanical Engineering
Biot problem
poroelasticity
Uncertainty Quantification
Polynomial Chaos expansions
Pseudo-Spectral Projection methods
Hybrid High-Order methods
Sparse grid
Numerical Analysis (math.NA)
Solver
Biot problem
Computer Science Applications
010101 applied mathematics
65C30
65M60
65M70
35R60
76S05
Mechanics of Materials
Probability distribution
Partial derivative
Uncertainty Quantification
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, 361, pp.112736. ⟨10.1016/j.cma.2019.112736⟩
ISSN: 0045-7825
DOI: 10.1016/j.cma.2019.112736⟩
Popis: In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the parameter-dependent problem by non-intrusive techniques based on Polynomial Chaos decompositions. We specifically focus on sparse spectral projection methods, which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients. The deterministic solver is based on a Hybrid High-Order discretization supporting general polyhedral meshes and arbitrary approximation orders. We numerically investigate the convergence of the probability error of the Polynomial Chaos approximation with respect to the level of the sparse grid. Finally, we assess the propagation of the input uncertainty onto the solution considering an injection-extraction problem.
30 pages, 15 Figures
Databáze: OpenAIRE
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