The Research Of The Nested Large Sparse Matrix Unsteady Iterative Method

Reservoir numerical simulation are always related to solve large sparse linear equations,find a fast and stable method for solving them is of great significance.Due to the size of engineering system of linear equations often is very huge,we usually use unsteady iteration method.Unsteady iterative methods contains GMRES(Generalized Residual Method)and Orthomin orthogonal minimization(Orthomin)method,etc.These iterative methods are often combined with a linear equation coefficient matrix precondition methods.Usually,the precondition matrix using incomplete LU factorization(ILU Factorization)to construct,this paper main work is how to construct nested factorization precondition matrix and combine it with unsteady iteration method,and compare these combination with ILU precondition method as matrix precondition,in some numeral case we can concluded that for nested large sparse matrix nested factorization method in computing speed and iteration convergence both have obvious advantages.This paper simply describes the general process of reservoir simulation,outlined by the model,the difference discrete to linear equations are obtained by the Newton iteration method.The structure characteristics of the coefficient matrix and the linear equations defines the nested structure.This article briefly reviews the general solution of linear equations,the steady-state iteration methods.Secondly,in this paper,we introduce the processes of GMRES method and Orthomin method.As main portion,this paper presents a nested factorization(Nest Factorization)precondition matrix constructing method and construct process,and the precondition method combined with GMRES method and Orthomin method for solving large sparse matrix.Based on the numerical examples,we can conclude that for nested large sparse equation,the nested precondition method have advantages in both iterative times and computing time.