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Multilayered poroelastic structures are found in many biological tissues such as cartilage and the cornea, and play a key role in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we…

Numerical Analysis · Mathematics 2025-07-15 Andrew Scharf , Martina Bukač , Sunčica Čanić

This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…

Numerical Analysis · Mathematics 2025-07-01 Po-Yi Wu

The discretization of fluid-poromechanics systems is typically highly demanding in terms of computational effort. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral…

Numerical Analysis · Mathematics 2024-07-16 Ivan Fumagalli , Nicola Parolini , Marco Verani

We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid and poroelastic subproblems in a fully explicit fashion,…

Numerical Analysis · Mathematics 2026-03-24 Yifan Wang , Jeonghun Lee , Suncica Canic

A parallel implementation of a compatible discretization scheme for steady-state Stokes problems is presented in this work. The scheme uses generalized moving least squares to generate differential operators and apply boundary conditions.…

Numerical Analysis · Mathematics 2021-04-30 Quang-Thinh Ha , Paul A. Kuberry , Nathaniel A. Trask , Emily M. Ryan

In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-09-03 Lev Kazakovtsev

In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium…

Numerical Analysis · Mathematics 2018-04-23 Jeonghun J. Lee , Eleonora Piersanti , Kent-Andre Mardal , Marie E. Rognes

We present a convergence analysis of the parallel-in-time integration method known as the Parareal algorithm for degenerate differential-algebraic systems arising from quasi-static Biot models, which govern coupled flow and deformation in…

Numerical Analysis · Mathematics 2026-01-22 Iñigo Jimenez-Ciga , Francisco Gaspar , Kundan Kumar , Florin A. Radu

An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…

Pattern Formation and Solitons · Physics 2009-11-07 P. M. Lushnikov

In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph (BJ) interface conditions. Three Robin-type boundary conditions and a modified weak…

Numerical Analysis · Mathematics 2022-06-14 Zheng Li , Feng Shi , Yizhong Sun , Haibiao Zheng

An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…

Numerical Analysis · Mathematics 2025-12-23 Xiaozhe Hu , Francisco J. Gaspar , Carmen Rodrigo

In this paper, we propose a multiphysics mixed finite element method with Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a multiphysics reformulation of poroelasticity part of the original problem by introducing…

Numerical Analysis · Mathematics 2021-12-24 Zhihao Ge , Jin'ge Pang , Jiwei Cao

The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled…

Numerical Analysis · Mathematics 2022-11-16 Emilie Eliseussen , Marie E. Rognes , Travis B. Thompson

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

Numerical Analysis · Mathematics 2026-02-24 Zhihao Ge , Wenshuai Hu

In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress…

Numerical Analysis · Mathematics 2018-02-06 Manuel Borregales , Kundan Kumar , Florin Adrian Radu , Carmen Rodrigo , Francisco José Gaspar

We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…

Optimization and Control · Mathematics 2018-04-02 Loris Cannelli , Francisco Facchinei , Vyacheslav Kungurtsev , Gesualdo Scutari

The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…

Analysis of PDEs · Mathematics 2020-07-27 Martin Gander , Félix Kwok , Julien Salomon

The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…

Numerical Analysis · Mathematics 2016-11-03 Mingchao Cai , Luca F. Pavarino

In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…

Numerical Analysis · Mathematics 2021-05-24 Erlend Storvik , Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…

Numerical Analysis · Mathematics 2017-01-04 Bogdan Opanchuk , Simon Kiesewetter , Peter D. Drummond