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

Fuente: arXiv
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Main Authors: Cai, Mingchao, Kuchta, Miroslav, Li, Jingzhi, Li, Ziliang, Mardal, Kent-Andre
Format: Preprint
Published: 2025
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author Cai, Mingchao
Kuchta, Miroslav
Li, Jingzhi
Li, Ziliang
Mardal, Kent-Andre
author_facet Cai, Mingchao
Kuchta, Miroslav
Li, Jingzhi
Li, Ziliang
Mardal, Kent-Andre
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_15292
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model
Cai, Mingchao
Kuchta, Miroslav
Li, Jingzhi
Li, Ziliang
Mardal, Kent-Andre
Numerical Analysis
65M60, 65F08, 65F10
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.
title Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model
topic Numerical Analysis
65M60, 65F08, 65F10
url https://arxiv.org/abs/2501.15292