

Preprint 19/2004
Adaptive Geometrically Balanced Clustering of
-Matrices
Lars Grasedyck, Wolfgang Hackbusch, and Sabine Le Borne
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Submission date: 15. Apr. 2004
Pages: 19
published in: Computing, 73 (2004) 1, p. 1-23
DOI number (of the published article): 10.1007/s00607-004-0068-0
Bibtex
MSC-Numbers: 65F05, 65F30, 65N38, 65N50
Keywords and phrases: hierarchical matrices, adaptive mesh refinement, boundary elements
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Abstract:
In previous papers, a class of (data-sparse) hierarchical
(-) matrices is introduced that can be used to efficiently
assemble and store stiffness matrices arising in boundary element applications.
In this paper, we develop and analyse modifications in the
construction of an
-matrix that will allow an efficient
application to problems involving adaptive mesh refinement.
In particular, we present a new clustering algorithm such that,
when an
-matrix has to be updated due to some adaptive
grid refinement, the majority of the
previously assembled matrix entries can be kept whereas only a few
new entries resulting from the refinement have to be computed.
We provide an efficient implementation of the necessary
updates and prove for the resulting
-matrix that
the storage requirements as well as the complexity of the
matrix-vector multiplication are almost linear, i.e.,
.