An Iterative Decoupled Algorithm with Unconditional Stability for Biot Model

2022/04/18 by Huipeng Gu, Gu, Huipeng, Mingchao Cai +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2204.08403

openalex publication_date 2022/04/18 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled algorithm, some time-extrapolation based decoupled algorithms, and an iterative decoupled algorithm. Our focus is the analysis of the iterative decoupled algorithm. It is shown that the convergence of the iterative decoupled algorithm requires no extra assumptions on physical parameters or stabilization parameters. Numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed method.

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