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
Received 20 June 2002;
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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
- 4. The primal substructuring method
- 5. The FETI method
- 6. A family of FETI derived preconditioners for the primal substructuring method
- 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
- 10. Summary and concluding remarks
- Acknowledgements
- References







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