Издание: Numerical Analysis and Its Applications. 6th International Conference, NAA 2016 (Lozenetz, Bulgaria, June 15-22, 2016). Revised Selected Papers. (Lecture Notes in Computer Science 10187)
Издатель: Springer Verlag
, Год издания: 2017
Страницы: 70-81
Аннотация
The compressibility of Schur complement matrices is the essential ingredient for H-matrix techniques, and is well understood for Laplace type problems. The Helmholtz case is more difficult: there are several theoretical results which indicate when good compression is possible with additional techniques, and in practice sometimes basic H-matrix techniques work well. We investigate the compressibility here with extensive numerical experiments based on the SVD. We find that with growing wave number k, the ɛ-rank of blocks corresponding to a fixed size in physical space of the Green's function is always growing like O(kα), with α ∈ [3/4, 1] in 2d and α∈ [4/3, 2] in 3d.
