- and ²-matrices for low and high frequency Helmholtz equation

Lehel Banjai and Wolfgang Hackbusch

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Submission date: 03. Mar. 2005
Pages: 24
published in: IMA journal of numerical analysis, 28 (2008) 1, p. 46-79 
DOI number (of the published article): 10.1093/imanum/drm001
Bibtex
with the following different title: Hierarchical matrix techniques for low- and high-frequency Helmholtz problems
MSC-Numbers: 65N38, 33J05
Keywords and phrases: helmholtz equation, bem, hierarchical matrices
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Abstract:
An approach is presented for the efficient manipulation of matrices arising from the Galerkin discretisation of boundary element operators for the Helmholtz equation. Using -matrix and -matrix techniques, different methods are proposed for the low frequency and high frequency regimes. In both cases the methods are numerically stable and are proved to have almost linear complexity for the storage and the cost of the matrix-vector multiplication. Problems that have aspects of both regimes pose no difficulty. The efficiency of the methods is demonstrated by numerical examples.