Schur Complement Based Preconditioners for Twofold and Block Tridiagonal Saddle Point Problems

作     者：Mingchao Cai Guoliang Ju Jingzhi Li 

作者机构：Department of MathematicsMorgan State UniversityBaltimoreMD 21251USA. Solid State R&D DepartmentShenzhen Tenfong Co.Ltd.Shenzhen 518055P.R.China. Department of MathematicsSouthern University of Science and TechnologyShenzhen 518055P.R.China. 

出 版 物：《Communications in Mathematical Research》 (数学研究通讯（英文版）)

年 卷 期：2024年第40卷第2期

页      面：214-244页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the NIH-RCMI(Grant No.347U54MD013376) the affliated project award from the Center for Equitable Artificial Intelligence and Machine Learning Systems at Morgan State University(Project ID 02232301) the National Science Foundation awards(Grant No.1831950).The work of G.Ju is supported in part by the National Key R&D Program of China(Grant No.2017YFB1001604) the National Natural Science Foundation of China(Grant No.11971221) the Shenzhen Sci-Tech Fund(Grant Nos.RCJC20200714114556020,JCYJ20170818153840322,JCYJ20190809150413261) the Guangdong Provincial Key Laboratory of Computational Science and Material Design(Grant No.2019B030301001) 

主　　题：Schur complement block tridiagonal systems positively stable preconditioners Routh-Hurwitz stability criterion. 

摘      要：In this paper,we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point *** type of the preconditioners are based on the nested(or recursive)Schur complement,the other is based on an additive type Schur complement after permuting the original saddle point *** analyze different preconditioners incorporating the exact Schur *** show that some of them will lead to positively stable preconditioned systems if proper signs are selected in front of the Schur *** positive-stable preconditioners outperform other preconditioners if the Schur complements are further approximated *** experiments for a 3-field formulation of the Biot model are provided to verify our predictions.