A Splitting Preconditioner for Generalized Saddle Point Problems

Based on the parameterized Uzawa methods, a new preconditioner for generalized saddle point problems is worked out. An analysis of the pretreated matrix finds that the eigenvalues of the preconditioned matrix will cluster about 0 and 1 when the parameter t → 0. Consequently, on the condition of the proper selection of a parameter, it can ensure a satisfactory convergence when some GMRES iterative methods are used in Krylov subspace. Numerical results of some Navier-Stokes problems are presented to illustrate the actual effect of the preconditioner.