Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model

TL;DR

This paper develops and analyzes two robust preconditioners for a complex thermo-poroelasticity model, ensuring effective numerical solutions despite large parameter variations and mesh refinements.

Contribution

It introduces two novel preconditioners for a four-field thermo-poroelasticity model, demonstrating their robustness and effectiveness through theoretical analysis and numerical experiments.

Findings

Preconditioners are robust against parameter variations.

Both preconditioners perform well under mesh refinement.

Numerical results validate theoretical robustness.

Abstract

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.