• search hit 53 of 145
Back to Result List

Numerical study of two-grid preconditioners for 1d elliptic problems with highly oscillating discontinuous coefficients

  • Abstract — Various advanced two-level iterative methods are studied numerically and compared with each other in conjunction with finite volume discretizations of symmetric 1-D elliptic problems with highly oscillatory discontinuous coefficients. Some of the methods considered rely on the homogenization approach for deriving the coarse grid operator. This approach is considered here as an alternative to the well-known Galerkin approach for deriving coarse grid operators. Different intergrid transfer operators are studied, primary consideration being given to the use of the so-called problemdependent prolongation. The two-grid methods considered are used as both solvers and preconditioners for the Conjugate Gradient method. The recent approaches, such as the hybrid domain decomposition method introduced by Vassilevski and the globallocal iterative procedure proposed by Durlofsky et al. are also discussed. A two-level method converging in one iteration in the case where the right-hand side is only a function of the coarse variable is introduced and discussed. Such a fast convergence for problems with discontinuous coefficients arbitrarily varying on the fine scale is achieved by a problem-dependent selection of the coarse grid combined with problem-dependent prolongation on a dual grid. The results of the numerical experiments are presented to illustrate the performance of the studied approaches.

Download full text files

Export metadata

Additional Services

Search Google Scholar
Metadaten
Author:O. Iliev, R. Lazarov, J. Willems
URN:urn:nbn:de:hbz:386-kluedo-15325
Series (Serial Number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (111)
Document Type:Report
Language of publication:English
Year of Completion:2007
Year of first Publication:2007
Publishing Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2008/05/28
Tag:oscillating coefficients; preconditioner; two-grid algorithm
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011