An Optimally Convergent parallel splitting Algorithm for the Multiple-Network Poroelasticity Model
Abstract
This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled Stokes-parabolic system. To efficiently solve this system, we propose a parallel splitting approach. In the first time step, a monolithic solver is used to solve all variables simultaneously. For subsequent time steps, the system is split into a Stokes subproblem and a parabolic subproblem. These subproblems are then solved in parallel using a stabilization technique. This parallel splitting approach differs from sequential or iterative decoupling, significantly reducing computational time. The algorithm is proven to be unconditionally stable, optimally convergent, and robust across various parameter settings. These theoretical results are confirmed by numerical experiments. We also apply this parallel algorithm to simulate fluid-tissue interactions within the physiological environment of the human brain.
Cite
@article{arxiv.2503.07178,
title = {An Optimally Convergent parallel splitting Algorithm for the Multiple-Network Poroelasticity Model},
author = {Jijing Zhao and Huangxin Chen and Mingchao Cai and Shuyu Sun},
journal= {arXiv preprint arXiv:2503.07178},
year = {2025}
}