Hierarchical Matrices based on a Weak Admissibility Criterion
Wolfgang Hackbusch, Boris N. Khoromskij,and Ronald Kriemann
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Submission date: 10. Jan. 2003 (revised version: April 2004)
published in: Computing, 73 (2004) 3, p. 207-243
DOI number (of the published article): 10.1007/s00607-004-0080-4
MSC-Numbers: 65F50, 65F30, 65F35, 65F10
Keywords and phrases: integral equations, bem, hierarchical matrices, weak admissibility
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In preceding papers, a class of hierarchical matrices has been developed which are data-sparse and allow to approximate integral and more general nonlocal operators with almost linear complexity. In the present paper, a weaker admissibility condition is described which leads to a coarser partitioning of the hierarchical matrix format. A coarser format yields smaller constants in the work and storage estimates and thus leads to a cheaper hierarchical matrix arithmetic. On the other hand, in the case of boundary element problem for one-dimensional manifolds, the new approach preserves the approximation power which is known from the standard admissibility criterion. Furthermore, the weak hierarchical matrix format allows to analyse the accuracy of the hierarchical matrix inversion and multiplication.