报告题目：Parameter-Free Preconditioning via Regularization for Efficient Iterative Solution of Nearly Singular Elasticity and Poroelasticity problems
报告人：王卓然 博士 堪萨斯大学
报告时间：2025年05月21日（星期三）9:30-10:30
报告地点: 腾讯会议：950 343 081
校内联系人：王瑞姝 wangrs_math@jlu.edu.cn
报告摘要：While block Schur complement preconditioning has been widely studied for saddle point systems, challenges remain when dealing with nearly singular systems arising from nearly incompressible elasticity and poroelasticity flows. For such systems, existing work focuses on developing preconditioners that are spectrally equivalent to the corresponding numerical algebraic system. Those preconditioners are effective by design; however, they are not efficient in general since they are slated to solve nearly singular systems.
In this talk, we will present a new approach for developing effective and parameter-free block Schur complement preconditioners for nearly singular saddle point systems. A key of this approach is to regularize original systems with inherent identities and construct preconditioners based on the resulting regularized systems. It will be shown these preconditioners are straightforward to construct and implement. Moreover, bounds on the eigenvalues of the preconditioned systems will be derived. The convergence of MINRES and GMRES applied to those systems will be analyzed and shown to be independent of locking parameters and mesh size. Numerical results in 2D and 3D will be presented.
报告人简介：王卓然博士，现为堪萨斯大学博士后，主要研究弱有限元方法和科学计算方法，在 《SIAM J. Sci. Comput.》《 J. Sci. Comput.》《 J. Comput. Appl. Math.》等杂志发表学术论文十余篇。
