New block triangular preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks (Q1036353)

Summary: We establish two types of block triangular preconditioners applied to linear saddle point problems with singular (1,1) block. These preconditioners are based on the results presented in a paper of \textit{T. Rees} and \textit{C. Greif} [SIAM J. Sci. Comput. 29, No.~5, 1992--2007 (2007; Zbl 1155.65048)]. We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter for practice. Finally, numerical experiments are reported to illustrate the efficiency of the presented preconditioners.