, Volume 74, Issue 3, pp 205–223 | Cite as

Adaptive Recompression of Open image in new window -Matrices for BEM

  • L. Grasedyck


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 Open image in new window -matrix, that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains 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 Open image in new window -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.

AMS Subject Classifications:

65F05 65F30 65F50 


Hierarchical matrices data-sparse approximations formatted matrix operations fast solvers preconditioning boundary elements 


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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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