报告题目：Stable Discretization and Robust Solvers for Poroelasticity
主 讲 人：Prof. Xiaozhe Hu
单 位：Tufts University
ZOOM ID：975 2011 3597
Poroelasticity models the processes of coupled deformable porous media flow which is crucial in many applications. In this talk, we first discuss the stability issue of the popular P1-RT0-P0 discretization of the three-field formulation for poroelasticity. We then propose a stabilization technique based on edge/face bubble function enrichment. This gives rise to discretizations that are uniformly stable with respect to the physical parameters and have the same number of degrees of freedom as the classical P1-RT0-P0 approach. We will also discuss the linear solvers developed for solving the large-scale and ill-conditioned linear systems of equations arising from such discretizations. More specifically, we generalize the traditional framework of block preconditioners on saddle point systems to poroelasticity and develop effective preconditioners that are robust with respect to the physical and discretization parameters. If time allows, we will briefly mention multigrid solvers as well. Preliminary numerical experiments are presented to support the theory and demonstrate the robustness of our discretizations and preconditioners.
Xiaozhe Hu is an Associate Professor in the Department of Mathematics at Tufts University. He received his Ph.D. in Computational Mathematics from Zhejiang University in 2009. He conducted a year of postdoctoral research at the Beijing International Center of Mathematical Research and then became a postdoctoral fellow in the Department of Mathematics at Pennsylvania State University in 2010. He served in the position of Research Assistant Professor at Penn State before joining Tufts in 2014. Hu's primary research interests are in numerical analysis and scientific computing, with an emphasis on the development, analysis, and implementation of numerical algorithms for solving partial differential equations and graph problems arising from different applications, such as multiphase flow in porous media, magnetohydrodynamics, bioinformatics, and machine learning. His algorithms have been used by commercial companies such as NVIDIA, China National Offshore Oil Company, and Petro-China. In 2016, his work received the Reimann-Liouville Award at the International Conference on Fractional Differentiation and Its Applications and his algorithm won the best performer of Disease Module Identification DREAM Challenges. He was a plenary speaker at the twenty-fourth International Conference on Domain Decomposition Methods in 2017. His research has been supported by the U.S. Department of Energy and the National Science Foundation.