Parameters Robust Parallelizable Iterative Decoupled Algorithms for Thermo-Poroelasticity with Nonlinear Convective Transport
Abstract
This paper presents several parallel iterative algorithms for the nonlinear thermo-poroelasticity. We introduce an auxiliary variable to transform the original model into a four-field formulation to overcome Poisson locking. The iterative idea is extended to linearize and decouple the four-field model. Different coupling strategies are employed among these three subproblems, combined with appropriately designed iteration settings, yielding distinct iterative parallel algorithms. Stabilization terms are incorporated into these algorithms to ensure parameter robustness in extreme situations. We derive error estimates and prove the convergence of these parallel iterative decoupled algorithms. Finally, numerical experiments are presented to compare the performance of the different parallel algorithms in extreme parameter settings, thereby validating their efficiency and robustness.
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BibTeX
@misc{li2026parameters,
title = {{Parameters Robust Parallelizable Iterative Decoupled Algorithms for Thermo-Poroelasticity with Nonlinear Convective Transport}},
author = {Ziliang Li and Jingzhi Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29668},
eprint = {2610.29668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29668},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Parameters Robust Parallelizable Iterative Decoupled Algorithms for Thermo-Poroelasticity with Nonlinear Convective Transport
AU - Ziliang Li
AU - Jingzhi Li
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29668
UR - https://arxiv.org/abs/2610.29668
AB - This paper presents several parallel iterative algorithms for the nonlinear thermo-poroelasticity. We introduce an auxiliary variable to transform the original model into a four-field formulation to overcome Poisson locking. The iterative idea is extended to linearize and decouple the four-field model. Different coupling strategies are employed among these three subproblems, combined with appropriately designed iteration settings, yielding distinct iterative parallel algorithms. Stabilization terms are incorporated into these algorithms to ensure parameter robustness in extreme situations. We derive error estimates and prove the convergence of these parallel iterative decoupled algorithms. Finally, numerical experiments are presented to compare the performance of the different parallel algorithms in extreme parameter settings, thereby validating their efficiency and robustness.
ER -