A Preconditioner for the Schur Complement Matrix

STORTI MARIO; DALCIN LISANDRO; PAZ RODRIGO; YOMMI ANDREA; SONZOGNI VICTORIO; NIGRO NORBERTO

ADVANCES IN ENGINEERING SOFTWARE

ELSEVIER

Año: 2006 vol. 37 p. 754 - 762

0965-9978

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 [1,2] can be found in works [3,4].