We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The model involves several parameters that can vary significantly in practical applications, posing a challenge for developing discretization techniques and solution algorithms that handle such variations effectively. We propose a four-field formulation and apply a conforming finite element discretization. The primary focus is on constructing and analyzing preconditioners for the resulting linear system. Two preconditioners are proposed: one involves regrouping variables and treating the 4-by-4 system as a 2-by-2 block form, while the other is directly constructed from the 4-by-4 coupled operator. Both preconditioners are demonstrated to be robust with respect to variations in parameters and mesh refinement. Numerical experiments are presented to demonstrate the effectiveness of the proposed preconditioners and validate their theoretical performance under varying parameter settings.

翻译：本文研究一种热-多孔弹性模型，该模型描述了非等温条件下弹性多孔材料变形与流体流动之间的相互作用。该模型涉及多个在实际应用中可能显著变化的参数，这对开发能够有效处理此类变化的离散化技术和求解算法提出了挑战。我们提出了一种四场表述并应用协调有限元离散化方法。研究重点在于为所得线性系统构造并分析预条件子。提出了两种预条件子：一种通过对变量重新分组，将4×4系统处理为2×2块形式；另一种则直接基于4×4耦合算子构造。两种预条件子均被证明对参数变化和网格细化具有鲁棒性。数值实验展示了所提预条件子的有效性，并在不同参数设置下验证了其理论性能。