Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods
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In this paper, the Biot problem with uncertain poroelastic coefficients is modeled using a finite set of parameters with prescribed probability distribution, and a deterministic solver is based on a Hybrid High-Order discretization supporting general polyhedral meshes and arbitrary approximation orders.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2020-04-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Polynomial chaos & Probability distribution.read more
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Journal ArticleDOI
HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
TL;DR: This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method, which implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions.
Journal ArticleDOI
An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods
TL;DR: A novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem is introduced and it rests on mild time regularity assumptions that can be derived from an appropriate weak formulation of the continuous problem.
Book ChapterDOI
A Hybrid High-Order Method for Multiple-Network Poroelasticity
TL;DR: Hybrid High-Order methods for multiple-network poroelasticity are developed, modelling seepage through deformable fissured porous media, designed to support general polygonal and polyhedral elements.
Journal ArticleDOI
HDGlab : An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB
TL;DR: HDGlab as discussed by the authors is an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method, which implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions.
Journal ArticleDOI
Generalized Polynomial Chaos Expansion for Fast and Accurate Uncertainty Quantification in Geomechanical Modelling
TL;DR: A surrogate model based on the generalized Polynomial Chaos Expansion (gPCE) is proposed as an approximation of the forward problem to efficiently compute the Sobol’ indices for the sensitivity analysis and greatly reduce the computational cost of the original ES and MDA formulations, also enhancing the accuracy of the overall prediction process.
References
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General Theory of Three‐Dimensional Consolidation
TL;DR: In this article, the number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three-dimensional problems.
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Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
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Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
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