Algebraic two-level preconditioners for the Schur complement method

L. M. Carvalho CERFACS - France and COPPE-UFRJ Brazil
carvalho@cos.ufrj.br

L. Giraud
CERFACS
42 av.Gaspard Coriolis
31057 Toulouse Cedex
luc.giraud@cerfacs.fr

P. Le Tallec
CEREMADE
Université Paris Dauphine
75 775 Paris Cedex 16

Abstract

The solution of elliptic problems is challenging on parallel distributed memory computers as their Green's functions are global. To address this issue, we present a set of preconditioners for the Schur complement domain decomposition method. They implement a global coupling mechanism, through coarse space components, similar to the one proposed in [3]. The definition of the coarse space components is algebraic, they are defined using the mesh partitioning information and simple interpolation operators. These preconditioners are implemented on distributed memory computers without introducing any new global synchronization in the preconditioned conjugate gradient iteration. The numericaland parallel scalability of those preconditioners is illustrated on two-dimensionalmodel examples that have anisotropy and/or discontinuity phenomena.

[3] J. H. Bramble, J. E. Pasciak, and A. H. Schatz. The construction of preconditioners for elliptic problems by substructuring I, Math. Comp., 47 (175): 103-134, 1986.

Key words : Domain decomposition, two-level preconditioning, Schur complement, parallel distributed computing, elliptic partial differential equations.


Contributed August 3, 1998.