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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
17/2004

Adaptive Recompression of $\cal H$-Matrices for BEM

Lars Grasedyck

Abstract

The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators requires special compression techniques. In this article we use a hierarchical low-rank approximation, the so-called ${\cal H}$-matrix, that approximates the dense stiffness matrix in admissible blocks (corresponding to domains where the underlying kernel function is smooth) by low rank matrices. The low rank matrices are assembled by the ACA+ algorithm, an improved variant of the well-known ACA method. We present an algorithm that can determine a coarser block structure that minimises the storage requirements (enhanced compression) and speeds up the arithmetic (e.g., inversion) in the ${\cal H}$-matrix format. This coarse approximation is done adaptively and on-the-fly to a given accuracy such that the matrix is assembled with minimal storage requirements while keeping the desired approximation quality. The benefits of this new recompression technique are demonstrated by numerical examples.

Received:
Apr 13, 2004
Published:
Apr 13, 2004
Keywords:
hierarchical matrices, preconditioning, boundary elements

Related publications

inJournal
2005 Repository Open Access
Lars Grasedyck

Adaptive recompression of \(\mathscr {H}\)-matrices for BEM

In: Computing, 74 (2005) 3, pp. 205-223