Two-level preconditioner via a rigid body-based aggregation for the Schur complement system

Abstract

Most aggregation multigrid (MG) methods employ rigid body modes in constructing the prolongators and are famous for fast convergence with good efficiency. However, it is nontrivial to extend these methods to the Schur complement (SC) system, which is a partitioned and condensed system, because the rigid body modes utilize the nodal coordinates. In this work, we proposed a prolongator in an explicit form by transforming the SC system into an alternative system. The two-level preconditioner derived from the proposed prolongator guaranteed the convergence to be the same as a two-level MG in a single-domain system. As demonstrated in a typical shell problem, the two-level preconditioner showed much faster convergence rate, which is estimated by the condition number based on the Lanczos connection, and also improved the dependency of the convergence on the size of elements and subdomains as compared with a single-level preconditioner. Copyright (C) 2008 John Wiley & Sons, Ltd.