%0 Journal Article
%T Compressed absorbing boundary conditions via matrix probing
%A Rosalie B¨¦langer-Rioux
%A Laurent Demanet
%J Mathematics
%D 2014
%I arXiv
%X Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an absorbing layer to an operator at the boundary by layer-stripping elimination of the exterior unknowns, but the linear algebra involved is costly. We propose to bypass the elimination procedure, and directly fit the surface-to-surface operator in compressed form from a few exterior Helmholtz solves with random Dirichlet data. The result is a concise description of the absorbing boundary condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter.
%U http://arxiv.org/abs/1401.4421v1