Parallel Multilevel Preconditioners

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Abstract
In this paper, we provide techniques for the development and analysis of parallel multilevel preconditioners for the discrete systems which arise in numerical approximation of symmetric elliptic boundary value problems. These preconditioners are defined as a sum of independent operators on a sequence of nested subspaces of the full approximation space. On a parallel computer, the evaluation of these operators and hence of the preconditioner on a given function can be computed concurrently.