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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: M. Papadrakakis, B.H.V. Topping
Chapter 3

Block Diagonal Preconditioners for the Schur Complement Method

L.M. Carvalho and L. Giraud

Centre Europeen de Recherche et de Formation Avancee en Calcul Scientifique (CERFACS), Toulouse, France

Full Bibliographic Reference for this chapter
L.M. Carvalho, L. Giraud, "Block Diagonal Preconditioners for the Schur Complement Method", in M. Papadrakakis, B.H.V. Topping, (Editors), "Innovative Computational Methods for Structural Mechanics", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 3, pp 55-76, 1999. doi:10.4203/csets.1.3
We present numerical methods for solving systems of linear equations originated from the discretisation of two-dimensional elliptic partial differential equations. We are interested in differential equations that describe hetrogeneous and anisotropic phenomena. We use a non-overlapping domain decomposition method for solving the linear systems. We describe new local preconditioners for the interface problems that have a numerical behaviour better than the block Jacobi preconditioner and almost the same computational complexity. We show a set of experiments for comparing the numerical performance of the local preconditioners.

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