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MiS Preprint

${\cal H}$- and ${\cal H}^2$-matrices for low and high frequency Helmholtz equation

Lehel Banjai and Wolfgang Hackbusch


An approach is presented for the efficient manipulation of matrices arising from the Galerkin discretisation of boundary element operators for the Helmholtz equation. Using $\cal H$-matrix and ${\cal H}^2$-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.

MSC Codes:
65N38, 33J05
helmholtz equation, bem, hierarchical matrices

Related publications

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