Volume 60, pp. 256-275, 2024.

A novel iterative time integration scheme for linear poroelasticity

Robert Altmann and Matthias Deiml

Abstract

Within this paper, we introduce and analyze a novel time-stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable. Depending on the coupling strength of the two equations, we explicitly quantify the required number of inner iteration steps to guarantee first-order convergence. By a number of numerical experiments we confirm the theoretical results and study the dependence of the inner iteration steps in terms of the coupling strength. Moreover, we compare our method to the well-known fixed-stress scheme.

Full Text (PDF) [570 KB], BibTeX

Key words

poroelasticity, semi-explicit time discretization, decoupling, iterative scheme

AMS subject classifications

65M12, 65M20, 65L80, 76S05

Links to the cited ETNA articles

[5]	Vol. 55 (2022), pp. 310-340 Jeremias Arf and Bernd Simeon: A space-time isogeometric method for the partial differential-algebraic system of Biot's poroelasticity model
[15]	Vol. 48 (2018), pp. 202-226 Qingguo Hong and Johannes Kraus: Parameter-robust stability of classical three-field formulation of Biot's consolidation model

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