Work

The Modified Double Shift-splitting Preconditioner for Nonsymmetric Generalized Saddle Point Problems From the Time-harmonic Maxwell Equations

Year: 2025

Type: article

Abstract: Recently, Fan, Zhu and Zheng [Computational and Applied Mathematics, 37(3), 3256-3266] proposed a generalized double shift-splitting (GDSS) preconditioner induced by a new matrix splitting method for nonsymmetric generalized saddle point problems, and gave the corresponding theoretical analysis and numerical experiments. In this paper, based on the generalized double shift-splitting (GDSS) preconditioner, we generalize the GDSS algorithms and further present the modified double shift-splitting (MDSS) preconditioner for nonsymmetric generalized saddle point problems having a nonsymmetric positive definite (1,1)-block and a positive definite (2,2)-block. Moreover, by similar theoretical analysis, we analyze the convergence conditions of the corresponding matrix splitting iteration methods and preconditioning properties of the MDSS preconditioned saddle point matrices. In final, one example is provided to confirm the effectiveness.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240279

Authors: Litao Zhang, Haochen Zhao, Guangxu Zhu, Xiaojing Zhang

Institutions: Zhengzhou University of Aeronautics, Henan Normal University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Zhengzhou University

Awards: G1637844665, G5615385849, G6809039717, G7916933814