Publisher's Synopsis
Excerpt from Iterative Substructuring Methods: The General Elliptic Case
In section 3, we establish, by using elementary arguments, that the performance of iterative substructuring methods must decline in the absence of a mechanism for global transportation of information. In that section, we also consider the simplest case of problems with intersecting cuts, namely second order problems in planar regions approximated by piecewise linear elements. By introducing an idea from multigrid methods, we derive an algorithm which turns out to be identical to one recently introduced by Bramble, Pasciak and Schatz An alternative algorithm, see Dryja [17] and Dryja, Proskurowski and Widlund is also described and estimates are given of the rate of convergence of these two algorithms.
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