This paper explores an iterative coupling approach to solve thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative coupling technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot's poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.

翻译：本文探讨了一种用于求解热孔弹性问题的迭代耦合方法，并以其作为高保真离散化方案，在基于投影的约化阶模型训练中引入有限元技术。解决多物理场耦合问题的主要挑战在于其复杂性和高昂的计算成本。本研究提出一种解耦迭代求解方法，结合约化阶建模技术，旨在提升计算算法的效率。我们采用的迭代耦合技术基于已广泛研究的Biot孔弹性固定应力分裂方案。通过利用该耦合迭代方案得到的解，约化阶模型采用额外的Galerkin投影到由适当正交分解获得的少量模态构成的约化基空间上。数值实验证明了所提算法的有效性，展示了其计算性能。