Abstract
The symmetric positive definite system arising from a finite element discretization of an elliptic boundary value problem can be solved efficiently using the preconditioned conjugate gradient method (cf. (Saad 1996)). In this chapter we discuss the class of additive Schwarz preconditioners, which has built-in parallelism and is particularly suitable for implementation on parallel computers. Many well-known preconditioners are included in this class, for example the hierarchical basis and BPX multilevel preconditioners, the two-level additive Schwarz overlapping domain decomposition pre-conditioner, and the BPS and Neumann-Neumann nonoverlapping domain decomposition preconditioners.
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© 2002 Springer Science+Business Media New York
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Brenner, S.C., Scott, L.R. (2002). Additive Schwarz Preconditioners. In: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3658-8_8
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DOI: https://doi.org/10.1007/978-1-4757-3658-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3660-1
Online ISBN: 978-1-4757-3658-8
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