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Computer Methods in Applied Mechanics and Engineering
Volume 192, Issues 35-36, 29 August 2003, Pages 3799-3830
 
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doi:10.1016/S0045-7825(03)00374-8    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2003 Elsevier B.V. All rights reserved.

The mosaic of high performance domain Decomposition Methods for Structural Mechanics: Formulation, interrelation and numerical efficiency of primal and dual methods

Yannis FragakisE-mail The Corresponding Author and Manolis PapadrakakisCorresponding Author Contact Information, E-mail The Corresponding Author

Institute of Structural Analysis and Seismic Research, National Technical University of Athens, 9, Iroon Polytechniou, Zografou Campus, GR-15780, Athens, Greece

Received 20 June 2002; 
revised 28 December 2002; 
accepted 19 May 2003. ;
Available online 22 July 2003.

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Abstract

A multitude of domain decomposition methods (DDM) for structural mechanics is available in the literature today. A unified framework for formulating primal and dual DDM is thus presented in this paper, aiming at providing a mathematical platform for a uniform treatment of high performance DDM in structural mechanics. A novel approach for developing new DDM from existing methods is also proposed and is applied to dual and primal methods. In the field of the FETI methods, this approach leads to a new category of methods derived from existing FETI variants. Furthermore, two alternative formulations of the balancing domain decomposition method are described, while interrelations between the introduced and existing methods are established. Finally, comparative numerical tests demonstrate the differences in the computational performance of the methods in question.

Subject-index terms: 28; 60; 63; 80

Article Outline

1. Introduction
2. Mapping subdomains on the global domain
2.1. Mapping displacements and applied loads of the subdomains
2.2. Mapping Lagrange multipliers on the subdomains
2.3. Connections between subdomain mapping matrices
3. Solving the local subdomain and interface problems
3.1. Solving the local subdomain problems
3.2. Solving the interface problem
4. The primal substructuring method
5. The FETI method
5.1. Preconditioners for the FETI method
5.2. Projection operators for the FETI method
6. A family of FETI derived preconditioners for the primal substructuring method
6.1. Connections of the FETI derived primal preconditioners with the FETI methods
7. The balancing domain decomposition method
7.1. A two-level primal substructuring method
7.2. A two-level primal preconditioner
7.3. Connection between the two-level primal formulations
8. Connection between the balancing domain decomposition method and the FETI method
9. Numerical performance of the introduced methods
9.1. A 3-D elasticity test problem
9.2. A semi-cylindrical panel problem
10. Summary and concluding remarks
Acknowledgements
References








 
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