Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
17/2005
${\cal H}$- and ${\cal H}^2$-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 $\cal H$-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.
