A class of block alternating splitting implicit iteration methods for double saddle point linear systems. Issue 1 (28th May 2022)

• Record Type: Journal Article
• Authors: Dou, Yan; Liang, Zhao‐Zheng
• Is Part Of: Numerical linear algebra with applications. Volume 30:Issue 1(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-05-28
• Subjects: block alternating splitting implicit iteration -- convergence analysis -- preconditioning -- saddle point problems; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2455
• Languages: English
• ISSNs: 1070-5325

Abstract

Abstract: In the framework of a special block alternating splitting implicit (BASI) iteration scheme for generalized saddle point problems, we establish some new iteration methods for solving double saddle point problems by means of a suitable partitioning strategy. Convergence analysis of the corresponding BASI iteration methods indicates that they are convergent unconditionally under certain weak requirements for the related matrix splittings, which are satisfied directly for our specific application to double saddle point problems. Numerical examples for liquid crystal director and time‐harmonic eddy current models are presented to demonstrate the efficiency of the proposed BASI preconditioners to accelerate the GMRES method.