Axelsson, Owe; Blaheta, Radim; Neytcheva, Maya Preconditioning of boundary value problems using elementwise Schur complements. (English) Zbl 1194.65047 SIAM J. Matrix Anal. Appl. 31, No. 2, 767-789 (2009). In the context of algebraic multilevel iteration, the authors propose an efficient technique for computing the Schur complement preconditioners. These are based on a two-by-two block decomposition of the matrix, and their approximations are computed by assembly of local (macroelement) Schur complements. Reviewer: Constantin Popa (Constanţa) Cited in 1 ReviewCited in 28 Documents MSC: 65F08 Preconditioners for iterative methods 65F10 Iterative numerical methods for linear systems 65F50 Computational methods for sparse matrices 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:preconditioning; two-by-two block partitioning; elementwise Schur complements; boundary value problems; algebraic multilevel iteration PDFBibTeX XMLCite \textit{O. Axelsson} et al., SIAM J. Matrix Anal. Appl. 31, No. 2, 767--789 (2009; Zbl 1194.65047) Full Text: DOI