A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation

It is well-known that two-level and multi-level preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a projection-type preconditioner to get rid of the effect of both small and large eigenvalues of the coefficient matrix; multi-level approaches arise by recursively applying the two-level technique within the projection step. In the literature, various such preconditioners are known, coming from the fields of deflation, domain decomposition, igrid. At first glance, these methods seem to be quite distinct; however, from an abstract point of view, they are closely related. The aim of this paper is to relate two-level PCG methods with symmetric two-grid (V(1,1)-cycle) preconditioners (derived from multigrid (MG) approaches), abstract form, to deflation m...

• Type: Journal
• Year: 2010
• Where: SIAMMAX
• Authors: J. M. Tang, S. P. MacLachlan, Reinhard Nabben, C. Vuik
• Keywords: Deflation, Preconditioner, SIAMMAX 2010, Two-level Pcg Methods