A general Uzawa-type method for a class of 2 × 2 block structure linear system. (15th September 2021)

• Record Type: Journal Article
• Authors: Miao, Shu-Xin; Zhang, Jing; Meng, Lingsheng
• Is Part Of: Computers & mathematics with applications. Volume 98(2021)
• Page Start: 181
• Page End: 200
• Publication Date: 2021-09-15
• Subjects: 2×2 block structure linear system -- Uzawa-type method -- Convergence -- Semi-convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.07.007
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Numerical methods for Navier-Stokes equation and elasticity problem lead to a class of 2 × 2 block structure linear system. Based on a general splitting for the (1, 1) block of coefficient matrix and the Uzawa method, we consider a general Uzawa-type method for solving this 2 × 2 block structure linear system in this paper. With different choices of splitting matrix, the proposed Uzawa-type method includes some existing Uzawa-type methods as its special cases. The convergence and semi-convergence of the proposed method for solving nonsingular and singular problems are studied, respectively. When the splitting matrix is used as a preconditioner, we analyze the spectral properties of the preconditioned matrix. Numerical results are presented to verify the efficiency of the proposed method.