With the widely application of the computer,many areas of science involve the large-scale numerical calculation of nonlinear equations,and these areas require high precision of numerical results.Therefore,finding a efficient and robustness method has become one of hot topics in the field of scientific computing.It is well known that the inexact Newton(IN)method is commonly used for solving the nonlinear partial differential equations.However,the inexact Newton method cannot efficiently solve some complex and highly nonlinear problems,such as the highly nonlinear radiation transport problem and the high Reynolds number incompressible flow problem.Hence,in this thesis,the inexact Newton method with preconditioned technique is applied to solve the above two types of physical problems.This thesis firstly reviews the classical INB(Inexact Newton method with Back-tracking)algorithm and its preconditioning techniques.Then two improved INB al-gorithms are studied,which include,the nonlinearly elimination preconditioned INB(INB-NE)algorithm and the parameter continuation preconditioned INB(INB-PC)algorithm.The basic idea of the nonlinear elimination algorithm is to modify the ap-proximate solution of the last step in every step of Newton iteration within a certain range of residuals,i.e,to eliminate some elements that cause the slow convergence of the Newton algorithm.On the other hand,the parameter continuation technique seeks a good initial estimate for the Newton algorithm,by using the numerical solution of the small parameter as the initial estimate of the large parameter.Then the INB-NE and INB-PC methods are applied to the incompressible flow problem with high Reynolds numbers and the highly nonlinear radiation transport problem,respectively.Numeri-cal results show that the proposed methods are effective and converge better than the traditional inexact Newton method. |