Semi-explicit integration of second order for weakly coupled poroelasticity

TL;DR

This paper presents a semi-explicit, second-order time-stepping scheme for linear poroelasticity that decouples the system for improved computational efficiency, supported by convergence analysis and numerical validation.

Contribution

It introduces a novel semi-explicit second-order scheme for poroelasticity that leverages a connection to delayed differential equations for convergence proof.

Findings

Scheme achieves second-order accuracy.

Decouples the system for computational efficiency.

Numerical experiments confirm theoretical convergence.

Abstract

We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves the computational efficiency. The construction and the convergence proof are based on the connection to a differential equation with two time delays, namely one and two times the step size. Numerical experiments confirm the theoretical results and indicate the applicability to higher-order schemes.