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，该方法在基于投影的降阶模型训练过程中，利用有限元作为高保真离散化手段。解决耦合多物理场问题的主要挑战之一在于其复杂性和高昂的计算成本。在本研究中，我们引入了一种解耦的迭代求解方案，并结合降阶建模，旨在提升计算算法的效率。所采用的迭代耦合技术基于已针对比奥孔隙弹性理论进行广泛研究的固定应力分裂格式。通过利用该耦合迭代方案获得的解，降阶模型采用额外的伽辽金投影方法，将解投影到由本征正交分解提取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，展示了其卓越的计算性能。