On preconditioning Schur complement and Schur complement preconditioning
The author discusses implementation strategies of a class of multilevel recursive incomplete LU preconditioners. These preconditioners are based on block incomplete LU factorization of the coefficient matrix \(A\) of the linear system. To construct such an algorithm, a sparse matrix, based on an incomplete LU factorization of the matrix \(A\), is constructed as a preconditioner. In the preconditioning process, the Schur complement matrices are formed. Two implementation strategies are presented, both use the Schur complement matrix to precondition the matrix \(A\). The Schur complement preconditioning strategy seems to converge in a smaller number of iterations than the preconditioning Schur complement strategy does. Numerical experiments are performed (a convection-diffusion problem using standard 5-point central difference discretization scheme and a fourth-order 9-point compact finite difference discretization scheme).
scientific article; zbMATH DE number 1476907