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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
8/2005

Why approximate $LU$ decompositions of finite element discretizations of elliptic operators can be computed with almost linear complexity

Mario Bebendorf

Abstract

Although the asymptotic complexity of direct methods for the solution of large sparse finite element systems arising from second-order elliptic partial differential operators is far from being optimal, these methods are often preferred over modern iterative methods. This is mainly due to their robustness. In this article it is shown that an (approximate) $LU$ decomposition exists and that it can be computed in the algebra of hierarchical matrices with almost linear complexity and with the same robustness as the classical $LU$ decomposition.

Received:
Jan 24, 2005
Published:
Jan 24, 2005
MSC Codes:
35C20, 65F05, 65F50
Keywords:
approximate $lu$ decomposition, non-smooth coefficients, hierarchical matrices

Related publications

inJournal
2007 Repository Open Access
Mario Bebendorf

Why finite element discretizations can be factored by triangular hierarchical matrices

In: SIAM journal on numerical analysis, 45 (2007) 4, pp. 1472-1494