Generalized Aitken-like Acceleration of the Schwarz Method
(and Introduction) In this paper, we present a family of domain decomposition based on Aitken like acceleration of the Schwarz method seen as an iterative procedure with linear rate of convergence. This paper is a generalization of the method first introduced in Garbey and Tromeur-Dervout  that was restricted to Cartesian grids. The general idea is to construct an approximation of the eigenvectors of the trace transfer operator associated to dominant eigenvalues and accelerate these components after few Schwarz iterates. We consider here examples with the finite volume approximation on general quadrangle meshes of Faille  and finite element discretization.
KeywordsDomain Decomposition Cartesian Grid General Quadrangle Dominant Eigenvalue Schwarz Method
Unable to display preview. Download preview PDF.
- J. Baranger, M. Garbey, and F. Oudin-Dardun. Acceleration of the Schwarz method: the cartesian grid with irregular space step case. Technical report, CDCSP (Center for the development of parallel scientific computing), 2003.Google Scholar
- M. Garbey. Acceleration of the Schwarz method for elliptic problems. submitted, 2003.Google Scholar
- M. Garbey and D. Tromeur-Dervout. Two level domain decomposition for multi-clusters. In T. Chan, T. Kako, H. Kawarada, and O. Pironneau, editors, 12th Int. Conf. on Domain Decomposition Methods, pages 325–339. DDM.org, 2001.Google Scholar
- B. F. Smith, P. E. Bjørstad, and W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.Google Scholar