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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping
Chapter 8

Parallel Algorithms for Time-harmonic Hyperbolic Problems

F. Magoulès

Office National d'Études et de Recherche Aérospatiales, Chatillon, France

Full Bibliographic Reference for this chapter
F. Magoulès, "Parallel Algorithms for Time-harmonic Hyperbolic Problems", in B.H.V. Topping, (Editor), "Computational Mechanics using High Performance Computing", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 8, pp 151-183, 2002. doi:10.4203/csets.9.8
In this chapter the classical domain decomposition methods to solve linear system of equations arising from the finite element discretization of elliptic partial differential equations are presented. Mainly the analysis of the model Helmholtz equation is considered in bounded domains with first order absorbing boundary conditions. The Schwarz algorithm and the Lagrange multipliers based domain decomposition methods are described in a common formalism and detailed in a continuous and a discrete approach. The main features of their numerical analysis and their distributed parallel implementation are also presented.

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