Convergence Analysis of a Global-in-Time Iterative Decoupled Algorithm for Biot’s Model
Year: 2025
Author: Huipeng Gu, Mingchao Cai, Jingzhi Li
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 778–803
Abstract
Biot’s model is a multiphysics model that describes the interaction of a poroelastic material with its interstitial fluid flow. In this study, we focus on investigating the convergence behavior of a global-in-time iterative decoupled algorithm based on a three-field formulation. During each iteration, the algorithm involves solving a reaction-diffusion subproblem across the entire temporal domain, followed by resolving a Stokes subproblem over the same time interval. This algorithm is recognized for its ”partially parallel-in-time” property, enabling the implementation of a parallel procedure when addressing the Stokes subproblem. We establish its global convergence with a new technique by confirming that the limit of the sequence of numerical solutions of the global-in-time algorithm is the numerical solution of the fully coupled algorithm. Numerical experiments validate the theoretical predictions and underline the efficiency gained by implementing the parallel procedure within the proposed global-in-time algorithm.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2024-0074
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 778–803
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Biot’s model a global-in-time algorithm linear convergence.
Author Details
Huipeng Gu Email
Mingchao Cai Email
Jingzhi Li Email