Global-basis two-level method for indefinite systems. Part 1: convergence studies

A robust two-level solver for high inde"nite system of equations arising from the "nite element discretization is developed. It is shown that the optimal coarse model is spanned by the spectrum of the highest eigenmodes of the smoothing iteration matrix. Convergence studies conducted on a model prolongation operator reveal pathological sensitivity to any deviation from the optimal coarse model