A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a global problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that share the interface. The aim of this work is to present a theoretical basis (regarding the behavior of Schur complement matrix spectra) and some simple numerical experiments conducted in a sequential environment as a motivation for adopting the proposed preconditioner. Efficiency, scalability, and implementation details on a production parallel finite element code [Sonzogni V, Yommi A, Nigro N, Storti M. A parallel finite element program on a Beowulf cluster. Adv Eng Software 2002;33(7-10):427-43; Storti M, Nigro N, Paz R, Dalcín L. PETSc-FEM: a general purpose, parallel, multi-physics FEM program, 1999-2006] can be found in works [Paz R, Storti M. An interface strip preconditioner for domain decomposition methods: application to hydrology. Int J Numer Methods Eng 2005;62(13):1873-94; Paz R, Nigro N, Storti M. On the efficiency and quality of numerical solutions in cfd problems using the interface strip preconditioner for domain decomposition methods. Int J Numer Methods Fluids, in press].
Bibliographical noteFunding Information:
This work has received financial support from Consejo Nacional de Investigaciones Cientí ficas y Técnicas (CONICET, Argentina, grants PIP 0198/98), Universidad Nacional del Litoral (Argentina, grants CAI+D 2000/43) and ANPCyT (Argentina, grants PICT 6973/99, PID-74/99, PICT Lambda/2003, PME 209/2003). We made extensive use of freely distributed software as GNU/Linux OS, MPI, PETSc, gcc compilers, Octave, Open-DX among many others.
- Domain decomposition methods
- Schur complement preconditioning
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