Print Email Facebook Twitter Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods Title Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods Author Tang, J.M. Nabben, R. Vuik, C. Erlangga, Y.A. Faculty Electrical Engineering, Mathematics and Computer Science Department Microelectronics & Computer Engineering Date 2009-01-27 Abstract For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding two-level preconditioner combines traditional and projection-type preconditioners to get rid of the effect of both small and large eigenvalues of the coefficient matrix. In the literature, various two-level PCG methods are known, coming from the fields of deflation, domain decomposition and multigrid. Even though these two-level methods differ a lot in their specific components, it can be shown that from an abstract point of view they are closely related to each other. We investigate their equivalences, robustness, spectral and convergence properties, by accounting for their implementation, the effect of roundoff errors and their sensitivity to inexact coarse solves, severe termination criteria and perturbed starting vectors Subject DeflationDomain decompositionMultigridConjugate gradientsTwo-grid schemesTwo-level preconditioningSPD matricesTwo-level PCG methods To reference this document use: http://resolver.tudelft.nl/uuid:e16cd586-3278-44ae-851c-99b29c0fc16c Publisher Springer ISSN 1573-7691 Source Journal of Scientific Computing, 39 (3), 2009 Part of collection Institutional Repository Document type journal article Rights (c) 2009 The Authors Files PDF tang-2009.pdf 732.25 KB Close viewer /islandora/object/uuid:e16cd586-3278-44ae-851c-99b29c0fc16c/datastream/OBJ/view