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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: F. Magoulès
Chapter 8

Algebraic Domain Decomposition Preconditioners

L. Giraud1 and R.S. Tuminaro2

1Parallel Algorithms and Optimization Group, LIMA-IRIT (UMR CNRS 5505), ENSEEIHT, Toulouse, France
2Computation, Computers and Mathematics Center, Sandia National Laboratories, Livermore CA, United States of America

Full Bibliographic Reference for this chapter
L. Giraud, R.S. Tuminaro, "Algebraic Domain Decomposition Preconditioners", in F. Magoulès, (Editor), "Mesh Partitioning Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 8, pp 189-218, 2007. doi:10.4203/csets.17.8
Keywords: algebraic preconditioners, matrix partitioning, mesh partitioning, overlapping techniques, non-overlapping approaches, two-level preconditioning.

In this chapter, some popular and well-known domain decomposition preconditioners are described from an algebraic perspective. Specific emphasis is given to techniques that are well-suited to the parallel solution of large-scale scientific applications and industrial numerical simulations. Some computational aspects related to their parallel implementation are also addressed. This chapter is not intended for specialists in domain decomposition but rather for scientists who have some knowledge of linear algebra and discretisation techniques and who would like an introduction to domain decomposition.

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