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Adaptive geometrically balanced clustering of ℋ-matrices
Publikationstyp
Journal Article
Date Issued
2004-05-21
Sprache
English
Journal
Volume
73
Issue
1
Start Page
1
End Page
23
Citation
Computing (Vienna/New York) 73 (1): 1-23 (2004-01-01)
Publisher DOI
Scopus ID
Publisher
Springer
In [8], a class of (data-sparse) hierarchical (ℋ-) 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 ℋ-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 ℋ-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 ℋ-matrix that the storage requirements as well as the complexity of the matrix-vector multiplication are almost linear, i.e., O(nlog(n)).
Subjects
Adaptive mesh refinement
Boundary elements
Data-sparse approximation
Hierarchical matrices
DDC Class
510: Mathematik