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For nonsymmetric block three-by-three singular saddle point problems arisingfrom 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, Analternating positive semi-definite splitting preconditioner for thethree-by-three block saddle point problems, Math. Commun. 26 (2021) 177-195)established an alternating positive semi-definite splitting (APSS) method. Inthis work, we analyse the semi-convergence of the APSS method for solving aclass of nonsymmetric block three-by-three singular saddle point problems. TheAPSS induced preconditioner is applied to improve the semi-convergence rate ofthe flexible GMRES (FGMRES) method. Experimental results are designated tosupport the theoretical results. These results show that the servedpreconditioner is efficient compared with FGMRES without a preconditioner.

Semi-convergence of the APSS method for a class of nonsymmetric three-by-three singular saddle point problems