Space Decomposition Preconditioners and Parallel Solvers

This paper uses the general framework of space decomposition — subspace correction for providing an overview of Schwarz-type preconditioners. The considered preconditioners are one-level and two-level Schwarz methods based on an overlapping domain decomposition, a two-level method with the coarse grid space created by aggregation and a new two-level method with interfaces in the coarse grid space. Beside the description and analysis, we discuss also some implementation details, the use of inexact subproblem solvers etc. The efficiency of preconditioners is illustrated by numerical examples.

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