A multilevel preconditioner for domain decomposition boundary systems

Abstract

In this note, we consider multilevel preconditioning of the reduced boundary systems which arise in non-overlapping domain decomposition methods. It will be shown that the resulting preconditioned systems have condition numbers which are bounded in the case of multilevel spaces on the whole domain and grow at most proportional to the number of levels in the case of multilevel boundary spaces without multilevel extensions into the interior.