Augmented Lagrangian Preconditioners For Solving A Class Of Nonsymmetric Saddle Point Problems

A lot of practical problems arising from scientific computing and engineering applications require to solve a large sparse saddle point linear system. However, it brings some challenges to solve this type of problems because of its indefinite and poor spectral properties. In this paper, we focus on a fast and efficient algorithm for solving this type of problems. The framework of this paper is as follows. First of all, we study the nonsingular saddle point linear system with the singular (1,1)-block. A few new block diagonal and block triangle preconditioners about augmented block Shur complement is constructed. And the eigenvalues and corresponding eigenvec-tors distributons are analyzed. Numerical experiments show that the algorithm is feasibile and effective. Secondly, Ron Estrin’s conclusion in maximally rank d-eficient situation is further generalized to the nonsymmetric saddle point system. Further, the eigenvalues and the minimal polynomials of the iteration matrix are described.