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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: F. Magoulès
Chapter 4

Algorithms and Theory for Substructuring and Domain Decomposition Methods

F. Magoulès1 and F.-X. Roux2

1Applied Mathematics and Systems Laboratory, Ecole Centrale Paris, Chatenay-Malabry, France
2ONERA, Châtillon, France

Full Bibliographic Reference for this chapter
F. Magoulès, F.-X. Roux, "Algorithms and Theory for Substructuring and Domain Decomposition Methods", in F. Magoulès, (Editor), "Mesh Partitioning Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 4, pp 89-118, 2007. doi:10.4203/csets.17.4
Keywords: substructuring, domain decomposition methods, iterative methods, direct methods, Schur complement, FETI, FETI-H.

In this chapter the basis of substructuring methods and the most classical domain decomposition methods are presented in an homogenous formulation. Algorithms and implementation details of each method are fully provided for the reader. First, parallel finite element matrix forming based on substructuring is introduced. Then the parallel iterative solution of the linear system is presented. Direct methods with parallel matrix factorisation based on substructuring are then detailed. Finally, several domain decomposition methods including the Schur complement method, the dual Schur complement method, the FETI method and the FETI-H method are described.

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