An Optimally Convergent parallel splitting Algorithm for the Multiple-Network Poroelasticity Model

Fuente: arXiv
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Auteurs principaux: Zhao, Jijing, Chen, Huangxin, Cai, Mingchao, Sun, Shuyu
Format: Preprint
Publié: 2025
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author Zhao, Jijing
Chen, Huangxin
Cai, Mingchao
Sun, Shuyu
author_facet Zhao, Jijing
Chen, Huangxin
Cai, Mingchao
Sun, Shuyu
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_07178
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Optimally Convergent parallel splitting Algorithm for the Multiple-Network Poroelasticity Model
Zhao, Jijing
Chen, Huangxin
Cai, Mingchao
Sun, Shuyu
Numerical Analysis
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.
title An Optimally Convergent parallel splitting Algorithm for the Multiple-Network Poroelasticity Model
topic Numerical Analysis
url https://arxiv.org/abs/2503.07178