The Research Of Splitting Iteration Algorithms For Solving Generalized Saddle Point Problems

In the field of science and engineering computing,the numerical solution of a class of special linear equations,that is saddle point problems(or generalized saddle point problems),is often involved,such as nuclear physics and fluid mechanics calculation,digital image processing,numerical weather prediction,power system network design model,electromagnetic field calculation etc..In general,the coefficient matrix of the saddle point equation is usually a large-scale and sparse matrix and often has some special properties.So far,to produce a variety of saddle point problems in the application of the model,many domestic and foreign researcher have conducted extensive research and obtained many effective numerical algorithms,such as Uzawa method,SOR-like method,HSS type method and preconditioning method etc..However,due to the complexity of the problem,there are not many effective numerical algorithms for solving the generalized saddle point problems.Therefore,our dissertation mainly studies the numerical solution of a class of generalized saddle point problems.A SOR-like iterative algorithm and a generalized AOR iterative(GAOR)algorithm are given by constructing the corresponding splitting of the saddle point coefficient matrix,and the convergence of the algorithms has been discussed.This dissertation is divided into four chapters as follows:In the first chapter,we introduce the research background,the common research methods and the preliminary knowledge of the saddle point problems and the generalized saddle point problems.In the second chapter,we construct a numerical method for solving the generalized saddle point problems.Based on the SOR-like splitting of the coefficient matrix,a new iterative algorithm for solving the generalized saddle point problems is given,and the convergence of the algorithm is studied.Finally,several numerical examples are given,and the result show that the new method is more effective than the PIU method.In the third chapter,we propose a GAOR algorithm for solving the generalizedsaddle point problem by constructing an appropriate splitting.Numerical results show that the new method outperforms the PIU method.The fourth chapter gives a summary of this dissertation and the prospects for future work.