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Multilevel Minimal Residual Methods for Nonsymmetric Elliptic Problems

✍ Scribed by Gerhard Starke

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
756 KB
Volume
3
Category
Article
ISSN
1070-5325

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✦ Synopsis

The subject of this paper is to study the performance of multilevel preconditioning for nonsymmetric elliptic boundary value problems. In particular, a minimal residual method with respect to an appropriately scaled norm, measuring the size of the residual projections on all levels, is studied. This norm, induced by the multilevel splitting, is also the basis for a proper stopping criterion. Our analysis shows that the convergence rate of this minimal residual method using the multilevel preconditioner by Bramble, Pasciak and Xu is bounded independently of the mesh-size. However, the convergence rate deteriorates with increasing size of the skew-symmetric part. Our numerical results show that by incorporating this into a multilevel cycle starting on the coarsest level, one can save fine-level-iterations and, therefore, computational work.

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