An iterative method for elliptic problems on regions partitioned into substructures

Bramble, J. H.; Pasciak, J. E.; Schatz, A. H.

doi:10.1090/S0025-5718-1986-0829613-0

An iterative method for elliptic problems on regions partitioned into substructures
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by J. H. Bramble, J. E. Pasciak and A. H. Schatz PDF

Math. Comp. 46 (1986), 361-369 Request permission

Abstract:

Some new preconditioners for discretizations of elliptic boundary problems are studied. With these preconditioners, the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains. Analytic estimates are given which guarantee that under appropriate hypotheses, the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns. Numerical examples are presented which illustrate the theoretically predicted iterative convergence rates.

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