Hybrid Cross Approximation of Integral Operators

Steffen Börm and Lars Grasedyck

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Submission date: 07. Oct. 2004 (revised version: March 2005)
Pages: 33
published in: Numerische Mathematik, 101 (2005) 2, p. 221-249 
DOI number (of the published article): 10.1007/s00211-005-0618-1
Bibtex
MSC-Numbers: 45B05, 65N38, 68P05
Keywords and phrases: hierarchical matrices, bem, interpolation
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Abstract:
The efficient treatment of dense matrices arising, e.g., from the finiteelement discretisation of integral operators, requires special compressiontechniques. In this article we use the -matrix representation thatapproximates the dense stiffness matrix in admissible blocks (correspondingto subdomains where the underlying kernel function is smooth) by low rankmatrices. The low rank matrices are assembled by a new hybrid algorithm(HCA) that has the same proven convergence as standard interpolation butalso the same efficiency as the (heuristic) adaptive cross approximation(ACA).