Article ID Journal Published Year Pages File Type
5775956 Applied Mathematics and Computation 2017 10 Pages PDF
Abstract
Based on a local generalized shift-splitting of the saddle point matrix with symmetric positive definite (1, 1)-block and symmetric positive semidefinite (2, 2)-block, a new local generalized shift-splitting preconditioner with two shift parameters for solving saddle point problems is proposed. The preconditioner is extracted from a new local generalized shift-splitting iteration and can lead to the unconditional convergence of the iteration. In addition, we consider solving the saddle point systems by preconditioned Krylov subspace methods and discuss some properties of the preconditioned saddle point matrix with a deteriorated preconditioner, such as eigenvalues, eigenvectors, and degree of the minimal polynomial. Numerical experiments arising from a finite element discretization model of the Stokes problem are given to validate the effectiveness of the proposed preconditioner.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
Authors
, ,