Recursive two-level ILU preconditioner for nonsymmetric M-matrices
The authors start from a block-LU decomposition of \(A\) (which is a \(2\times 2\) block matrix, possibly approximating a partial differential equation on two grids or on one grid with an ordering of the points into fine and coarse ones) and approximate this LU decomposition by approximating the pivot block, its inverse (for use in an approximate Schur complement \(S\)) and by possibly skipping off-diagonal elements of \(S\). They show for M-matrices \(A\) [referring often to \textit{O. Axelsson}'s book: Iterative solution methods (1994; Zbl 0795.65014)] that this scheme works recursively (after \(A\), \(S\) is \(2\times 2\) block decomposed etc.) under appropriate conditions on the approximations. The English of the paper is curious at places but the authors make a good job in presenting 3 diagonal approximations of the inverse of the pivot which are easy to compute and satisfy the conditions. Numerical results are reasonable and concern 2D convection diffusion problems approximated by an upwind difference scheme.
scientific article; zbMATH DE number 2111237
scientific article