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报告摘要： Thermo-poroelastic models capture the interplay between elastic porous material deformation, fluid flow, and thermal effects under non-isothermal conditions. This talk presents a four-field formulation for the linear thermo-poroelastic model and introduces two novel algorithms. The first focuses on constructing parameter-robust preconditioners for the resulting linear system, proposing two approaches: one reorganizes variables into a 2-by-2 block structure, while the other directly addresses the 4-by-4 coupled operator. Both preconditioners exhibit robustness to parameter variations and mesh refinement. The second algorithm is a decoupled iterative finite element method, for which stability and optimal convergence are rigorously proven. Numerical experiments are provided to validate the effectiveness and efficiency of the proposed methods.
报告人简介： 蔡明超, 美国马里兰摩根州立大学教授, 博导. 主要从事数值分析, 流体, 弹性和生物力学的计算. 尤其在多物理和多区域问题的建模与计算方面成果丰硕, 学术造诣深厚. 在SINUM, SISC, Math. Comput., Journal of Biomechanical Engineering, ASME, 以及 J. Biomechanics 等国际顶级 SCI 期刊上发表 40 余篇论文, 出版 book chapters 2 部, 受邀出席各类学术会议并作大会报告、特邀报告 80 余次; 担任《MathSciNet》及 40 余种计算数学、计算物理、计算生物力学领域权威期刊审稿专家; 曾牵头组织并主持国际学术会议CBMS Conference: Deep Learning and Numerical PDEs (2023), 学术影响力广泛。
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