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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
17/2005

H- and H2-matrices for low and high frequency Helmholtz equation

Lehel Banjai and Wolfgang Hackbusch

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 H-matrix and H2-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.

Contact the author per mail Download full preprint 332 KB
Received:
03.03.05
Published:
03.03.05
MSC Codes:
65N38, 33J05
Keywords:
helmholtz equation, bem, hierarchical matrices

Related publications

inJournal
2008 Repository Open Access
Lehel Banjai and Wolfgang Hackbusch

Hierarchical matrix techniques for low- and high-frequency Helmholtz problems

In: IMA journal of numerical analysis, 28 (2008) 1, pp. 46-79
BibTex DOI: 10.1093/imanum/drm001