A numerical study of some parallel algebraic preconditioners

We present a numerical study of several parallel algebraic preconditioners, which speed up the convergence of Krylov iterative methods when solving large-scale linear systems. The studied algebraic preconditioners are of two types. The first type includes simple block preconditioners using incomplete factorizations or preconditioned Krylov solvers on the subdomains. The second type is an enhancement of the first type in that Schur complement techniques are added to treat subdomain-interface unknowns. The numerical experiments show that the scalability properties of the preconditioners are highly problem dependent, and a simple Schur complement technique is favorable for achieving good overall efficiency.