A New Class Of Splitting Preconditioned Iterative Methods For Solving The Optimal Control Of The Stokes Equations

Based on the coefficient matrix. there are many techniques of constructing pre-conditioners, such as the matrix splitting method for splitting preconditioners. In recent years, the optimal control constrained by the Stokes equations have received considerable attentions. In this thesis, we will give a new class of splitting precon-ditioners for iteratively solving the saddle point problems arising from the optimal control problems.We first introduce the finite element discrete process of the optimal control problems constrained by the Stokes equations. Secondly, to iteratively solve the obtained linear saddle point system efficiently, we give a class of splitting precondi-tioners. Based on the modified dimension splitting preconditioner PMDS in [19], we provide a new class of splitting preconditioner P₁, its generalized forms and accel-erated splitting preconditioner P₂. In theory, we analyze their spectral properties. Finally, numerical results are given to illustrate the efficiency of the new class of splitting preconditioners.The contributions of this thesis include:?1? Based on the modified dimension splitting preconditioner P_MDS in [19], a new class of splitting preconditioner P₁ is given to solve the optimal control problem constrained by the Stokes equations efficiently.?2? The generalized splitting forms and accelerated splitting preconditioner P₂ are proposed.