This paper explores an iterative coupling approach to solve linear 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：本文探讨了一种求解线性热-孔隙弹性问题的迭代耦合方法，并在基于投影的降阶模型训练过程中，将其作为采用有限元的高保真离散化手段。处理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。本研究引入了一种解耦的迭代求解方案，并与降阶建模相结合，旨在提升计算算法的效率。我们所采用的迭代耦合技术建立在经过充分研究的固定应力分裂方案基础之上，该方案已广泛用于Biot孔隙弹性问题。通过利用该耦合迭代方案得出的解，降阶模型采用额外的伽辽金投影，将解投影到一个由通过本征正交分解获得的少量模态构成的降阶基空间上。数值实验验证了所提算法的有效性，展示了其强大的计算能力。