Numerical Method Of The Saddle Point Problem

In this thesis, we discuss numerical method of the saddle point problems. These problems arise in numerous applications such as fluid dynamics, constraint quadratic programming, linear elasticity, electromagnetic and other areas of applications an so on. Since the coefficient matrices of these problems usually are large and sparse, it is useful to consider some fast numerical methods. There are large variety methods for solving these linear systems, such as direct solvers, Uzawa type algorithms, Null-space methods and Krylov subspace methods. In this thesis, first, we review some existing algorithms. To accelerate the convergence speed, we propose new exact algorithm and inexact algorithm for symmetric and nonsymmetric saddle point problems. we have also considered the convergence properties and given some theorems and conclusions. Numerical experiments show that this new method is feasible and effective. Finally, we extend the special preconditioner to a class preconditioner, and discuss convergence properties and parameter choice.