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Related papers: Robust block preconditioners for poroelasticity

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In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused…

Numerical Analysis · Mathematics 2022-12-19 Hyun C. Yoon , S. M. Mallikarjunaiah , Dambaru Bhatta

We consider the variational formulation of both geometrically linear and geometrically nonlinear elasto-plasticity subject to a class of hard single-slip conditions. Such side conditions typically render the associated boundary-value…

Analysis of PDEs · Mathematics 2015-06-18 Keith Anguige , Patrick W. Dondl

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner…

Numerical Analysis · Mathematics 2011-07-13 Blanca Ayuso De Dios , Michael Holst , Yunrong Zhu , Ludmil Zikatanov

Using the framework of operator or Cald\'{e}ron preconditioning, uniform preconditioners are constructed for elliptic operators of order $2s \in [0,2]$ discretized with continuous finite (or boundary) elements. The cost of the…

Numerical Analysis · Mathematics 2020-04-15 Rob Stevenson , Raymond van Venetië

The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…

Optimization and Control · Mathematics 2025-05-21 Shaohui Yang , Toshiyuki Ohtsuka , Brian Plancher , Colin N. Jones

A stable finite element scheme that avoids pressure oscillations for a three-field Biot's model in poroelasticity is considered. The involved variables are the displacements, fluid flux (Darcy velocity), and the pore pressure, and they are…

Numerical Analysis · Mathematics 2016-05-03 Xiaozhe Hu , Carmen Rodrigo , Francisco J. Gaspar , Ludmil T. Zikatanov

We propose an efficient iterative method to solve the mixed Stokes-Dracy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of…

Numerical Analysis · Mathematics 2012-08-09 Antonio Márquez , Salim Meddahi , Francisco-Javier Sayas

We study numerical methods for solving reactive transport problems in porous media that allow a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. After recalling…

Numerical Analysis · Mathematics 2018-10-12 Laila Amir , Michel Kern

This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about…

Numerical Analysis · Mathematics 2021-10-08 Eisa Khosravi Dehdezi , Saeed Karimi

In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed…

Numerical Analysis · Mathematics 2016-08-24 Francesc Verdugo , Wolfgang A. Wall

We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…

Numerical Analysis · Mathematics 2025-10-28 Kangan Li , Yashar Mehmani

In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and…

Numerical Analysis · Mathematics 2013-04-08 Bin Zheng , Guang Lin , Jinchao Xu

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…

Numerical Analysis · Mathematics 2013-02-18 Xiaozhe Hu , Shuhong Wu , Xiao-Hui Wu , Jinchao Xu , Chen-Song Zhang , Shiquan Zhang , Ludmil Zikatanov

We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to…

Computational Engineering, Finance, and Science · Computer Science 2016-01-26 A. E. Kolesov , P. N. Vabishchevich

In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are…

Numerical Analysis · Mathematics 2024-01-01 Johannes Kraus , Kundan Kumar , Maria Lymbery , Florin Adrian Radu

We analyze a weak formulation of the coupled problem defining the interac- tion between a free fluid and a poroelastic structure. The problem is fully dynamic and is governed by the time-dependent incompressible Navier-Stokes equations and…

Analysis of PDEs · Mathematics 2022-05-25 Aycil Cesmelioglu

We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass…

Numerical Analysis · Mathematics 2021-12-16 Tongtong Li , Ivan Yotov

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

Numerical Analysis · Mathematics 2018-12-27 Robert Altmann , Eric Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

Numerical Analysis · Mathematics 2023-10-26 Fatemeh P. A. Beik , Michele Benzi