On the indefinite Helmholtz equation: complex stretched absorbing boundary layers, iterative analysis, and preconditioning
Numerical Analysis
2010-08-19 v2
Abstract
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This results into a preconditioner problem that is invertible with a multigrid cycle. We give a numerical analysis based on the eigenvalues and evaluate the performance with several numerical experiments. The method is an alternative to the complex shifted Laplacian and it gives a comparable performance for the studied model problems.
Cite
@article{arxiv.0912.0180,
title = {On the indefinite Helmholtz equation: complex stretched absorbing boundary layers, iterative analysis, and preconditioning},
author = {Bram Reps and Wim Vanroose and Hisham bin Zubair},
journal= {arXiv preprint arXiv:0912.0180},
year = {2010}
}