Krylov subspace methods
GMRES, nonsymmetric elliptic problems
Wiley InterScience Backfile Collection 1832-2000
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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