Homotopy Perturbation Numerical Method For Saddle Point Problems

In this thesis, we propose a new 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. 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. X.Feng and etc apply modified homotopy perturbation method for solving the augmented systems. In this thesis, we extend this method to general saddle point problems. By construct different auxiliary system, the original non definite system was converted to a serial of simple system. we propose a class of new iterative algorithm and derive the sufficient and necessary conditions for guarantee convergence. Numerical experiments show the method's correctness and efficiency.