Semi-convergence of the APSS method for a class of nonsymmetric three-by-three singular saddle point problems
Abstract
For nonsymmetric block three-by-three singular saddle point problems arising from the Picard iteration method for a class of mixed finite element scheme, recently Salkuyeh et al. in (D.K. Salkuyeh, H. Aslani, Z.Z. Liang, An alternating positive semi-definite splitting preconditioner for the three-by-three block saddle point problems, Math. Commun. 26 (2021) 177-195) established an alternating positive semi-definite splitting (APSS) method. In this work, we analyse the semi-convergence of the APSS method for solving a class of nonsymmetric block three-by-three singular saddle point problems. The APSS induced preconditioner is applied to improve the semi-convergence rate of the flexible GMRES (FGMRES) method. Experimental results are designated to support the theoretical results. These results show that the served preconditioner is efficient compared with FGMRES without a preconditioner.
Keywords
Cite
@article{arxiv.2208.00814,
title = {Semi-convergence of the APSS method for a class of nonsymmetric three-by-three singular saddle point problems},
author = {Hamed Aslani and Davod Khojasteh Salkuyeh},
journal= {arXiv preprint arXiv:2208.00814},
year = {2022}
}
Comments
17 pages, submitted