A comparison of overlapping Schwarz methods and block preconditioners for saddle point problems

Three domain decomposition methods for saddle point problems are introduced and compared. The first two are block-diagonal and block-triangular preconditioners with diagonal blocks approximated by an overlapping Schwarz technique with positive definite local and coarse problems. The third is an overlapping Schwarz preconditioner based on indefinite local and coarse problems. Numerical experiments show that while all three methods are numerically scalable, the last method is almost always the most efficient.