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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
78/2005

On the numerical solution of convection-dominated problems using hierarchical matrices

Mario Bebendorf

Abstract

The aim of this article is to shows that hierarchical matrices ($\H$-matrices) provide a means to efficiently precondition linear systems arising from the streamline diffusion finite-element method applied to convection-dominated problems. Approximate inverses and approximate $LU$ decompositions can be computed with logarithmic-linear complexity in the standard $\H$-matrix format. Neither the complexity of the preconditioner nor the number of iterations will depend on the dominance. Although the established theory is only valid for irrotational convection, numerical experiments show that the same efficiency can be observed for general convection terms.

Received:
Sep 2, 2005
Published:
Sep 2, 2005
MSC Codes:
35C20, 65F05, 65F50
Keywords:
singularly perturbed problems, preconditioners, hierarchical matrices

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Preprint
2005 Repository Open Access
Mario Bebendorf

On the numerical solution of convection-dominated problems using hierarchical matrices