An algebraic two-level preconditioner for asymmetric, positive-definite systems

A two-level, linear algebraic solver for asymmetric, positive-definite systems is developed using matrices arising from stabilized finite element formulations to motivate the approach. Supported by an analysis of a representative smoother, the parent space is divided into oscillatory and smooth subspaces according to the eigenvectors of the associated normal system. Using a mesh-based aggregation technique, which relies only on information contained in the matrix, a restriction/prolongation operator is constructed. Various numerical examples, on both structured and unstructured meshes, are performed using the two-level cycle as the basis for a preconditioner. Results demonstrate the complementarity between the smoother and the coarse-level correction as well as convergence rates that are nearly independent of the problem size. Copyright (C) 2001 John Wiley & Sons, Ltd.