The swiss-carpet domain decomposition preconditioner

MOX 44
The swiss-carpet domain decomposition preconditioner
Monday 28th June 2004
Quarteroni, Alfio; Sala, Marzio; Valli, Alberto
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In this paper we consider domain decomposition preconditioners based on a vertex-oriented decomposition of the computational domain. In element-oriented (EO) decompositions, each element of the grid belongs to a different domain, while in vertex-oriented (VO) decompositions each vertex belongs to a different subdomain. Based on VO decompositions, we present several preconditioners for the solution of the original (unreduced) system, as well as for that of the Schur complement system. Theoretical properties are investigated for a finite element approximation of a scalar problem. Numerical results and comparison with state-of-art preconditioners are also reported. The numerical results here presented show the effectiveness of the proposed preconditioners and their good parallel properties.