An efficient implementation of certain iterative refinement preconditioners
The BEPS preconditioner cf. \textit{J. H. Bramble, R. E. Ewing, J. E. Pasciak} and \textit{A. H. Schatz} [Comput. Methods Appl. Mech. Eng. 67, No. 2, 149-159 (1988; Zbl 0632.76112)] was suggested to solve linear systems arising from the discretization of elliptic or parabolic problems on grids with local refinement. This paper is concerned with an efficient implementation of the BEPS preconditioner for the preconditioned conjugate gradient (CG) method or in the case of unsymmetric system matrices for the preconditioned variants of the generalized conjugate gradient -- least squares (GCG-LS) or the generalized minimal residual (GMRES) methods. The efficient implementation is based on exploiting the sparsity pattern of residuals with nonzero entries appearing only on the interface between the coarse grid and the local fine grid.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 519761
scientific article