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

A two-level, linear algebraic solver for asymmetric, positive-definite syst ems is developed using matrices arising from stabilized finite element form ulations to motivate the approach. Supported by an analysis of a representa tive smoother, the parent space is divided into oscillatory and smooth subs paces according to the eigenvectors of the associated normal system. Using a mesh-based aggregation technique, which relies only on information contai ned in the matrix, a restriction/prolongation operator is constructed. Vari ous numerical examples, on both structured and unstructured meshes, are per formed 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.