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., .