Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

DOI10.1007/s13137-021-00180-4zbMath1480.65260arXiv2101.11810OpenAlexW3176980619MaRDI QIDQ2059122

Teeratorn Kadeethum, Nikolaos Bouklas, Francesco Ballarin

Publication date: 13 December 2021

Published in: GEM - International Journal on Geomathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.11810

zbMATH Keywords

neural networksfinite elementheterogeneityreduced order modelingdiscontinuous Galerkinporoelasticity

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Flows in porous media; filtration; seepage (76S05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

• Unnamed Item
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• A nonlinear, transient finite element method for coupled solvent diffusion and large deformation of hydrogels
• Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits
• On a coupled discontinuous/continuous Galerkin framework and an adaptive penalty scheme for poroelasticity problems
• A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces
• Convergence of iterative coupling for coupled flow and geomechanics
• Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism
• Data-driven POD-Galerkin reduced order model for turbulent flows
• Implicit \(r\)-point block backward differentiation formula for solving first-order stiff ODEs
• Model order reduction: Theory, research aspects and applications. Selected papers based on the presentations at the workshop `Model order reduction, coupled problems and optimization', Leiden, The Netherlands, September 19--23, 2005.
• Reduced order models based on local POD plus Galerkin projection
• A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity
• Local flux mimetic finite difference methods
• Non-intrusive reduced order modeling of nonlinear problems using neural networks
• Coupling multipoint flux mixed finite element methods with continuous Galerkin methods for poroelasticity
• POD-Galerkin reduced order methods for CFD using finite volume discretisation: vortex shedding around a circular cylinder
• A domain decomposition non-intrusive reduced order model for turbulent flows
• Enriched Galerkin finite elements for coupled poromechanics with local mass conservation
• Randomized model order reduction
• A five-field finite element formulation for nearly inextensible and nearly incompressible finite hyperelasticity
• Data-driven nonintrusive reduced order modeling for dynamical systems with moving boundaries using Gaussian process regression
• A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
• An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques
• Enriched Galerkin discretization for modeling poroelasticity and permeability alteration in heterogeneous porous media
• Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
• Multiscale finite volume method for finite-volume-based simulation of poroelasticity
• An artificial neural network framework for reduced order modeling of transient flows
• Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
• Finite element solvers for Biot's poroelasticity equations in porous media
• On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis
• Randomized linear algebra for model reduction. I. Galerkin methods and error estimation
• Cam-Clay plasticity. VIII: A constitutive framework for porous materials with evolving internal structure
• Stabilized material point methods for coupled large deformation and fluid flow in porous materials
• Cracking and damage from crystallization in pores: coupled chemo-hydro-mechanics and phase-field modeling
• A weighted POD method for elliptic PDEs with random inputs
• Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization
• Continuous block backward differentiation formula for solving stiff ordinary differential equations
• Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model
• Poromechanics of freezing materials
• Non-intrusive reduced order modelling of the Navier-Stokes equations
• A coupling of mixed and continuous Galerkin finite element methods for poroelasticity. I: The continuous in time case
• Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations
• PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Cell‐centered finite volume discretizations for deformable porous media
• An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models
• Reducing the Dimensionality of Data with Neural Networks
• Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
• Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes
• Hierarchical Approximate Proper Orthogonal Decomposition
• Phase-Field Modeling of Two Phase Fluid Filled Fractures in a Poroelastic Medium
• Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation
• Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity
• An Artificial Compression Reduced Order Model
• Discrete Inverse Problems
• Reservoir Simulation

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