Abstract
The paper describes domain decomposition methods of the Schwarz type with coarse problems constructed algebraically by aggregation of unknowns. The description includes a new method with no overlap of subdomains and interfaces on the coarse grid. Implementation issues are discussed for all the methods and their comparison is made on a model elasticity problem. Special attention is given to nonsymmetric hybrid preconditioners. A parallel implementation of the additive Schwarz method is tested on a 3D elasticity problem, employing a Beowulf cluster.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blaheta, R.: A multilevel method with overcorrection by aggregation for solving discrete elliptic problems. J. Comp. Appl. Math. 24, 227–239 (1988)
Blaheta, R.: GPCG – generalized preconditioned CG method and its use with non-linear and non-symmetric displacement decomposition preconditioners. Numer. Linear Algebra Appl. 9, 527–550 (2002)
Blaheta, R.: Space decomposition Preconditioners and Parallel Solvers. In: Feistauer, M., et al. (eds.) Numerical Mathematics and Advanced Applications, pp. 20–38. Springer, Berlin (2004)
Toselli, A., Widlund, O.: Domain Decomposition Methods – Algorithms and Theory. Springer, Berlin (2005)
Smith, B.F., Bjørstad, P.E., Gropp, W.D.: Domain Decomposition – Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, Cambridge (1996)
Saad, Y.: Iterative methods for sparse linear systems. SIAM, Philadelphia (2003)
Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, 2nd edn. Springer, New York (2002)
Brezina, M.: Robust iterative methods on unstructured meshes. PhD. thesis, University of Colorado at Denver (1997)
Jenkins, E.W., Kelley, C.T., Miller, C.T., Kees, C.E.: An aggregation-based domain decomposition preconditioner for groundwater flow. SIAM J. Sci. Comput. 23, 430–441 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blaheta, R., Byczanski, P., Jakl, O., Starý, J. (2006). Parallel Schwarz Methods: Algebraic Construction of Coarse Problems, Implementation and Testing. In: Wyrzykowski, R., Dongarra, J., Meyer, N., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2005. Lecture Notes in Computer Science, vol 3911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11752578_61
Download citation
DOI: https://doi.org/10.1007/11752578_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34141-3
Online ISBN: 978-3-540-34142-0
eBook Packages: Computer ScienceComputer Science (R0)