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

作　　者：Mingchao Cai Guoliang Ju Jingzhi Li 

机构地区：[1]Department of Mathematics,Morgan State University,Baltimore,MD 21251,USA. [2]Solid State R&D Department,Shenzhen Tenfong Co.Ltd.,Shenzhen 518055,P.R.China. [3]Department of Mathematics,Southern University of Science and Technology,Shenzhen 518055,P.R.China.

出　　处：《Communications in Mathematical Research》2024年第2期214-244,共31页数学研究通讯（英文版）

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).

摘　　要：In this paper,we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems.One 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 systems.We analyze different preconditioners incorporating the exact Schur complements.We show that some of them will lead to positively stable preconditioned systems if proper signs are selected in front of the Schur complements.These positive-stable preconditioners outperform other preconditioners if the Schur complements are further approximated inexactly.Numerical experiments for a 3-field formulation of the Biot model are provided to verify our predictions.

关 键 词：Schur complement block tridiagonal systems positively stable preconditioners Routh-Hurwitz stability criterion. 

分 类 号：O186.11[理学—数学]