New preconditioners for Laplace and Helmholtz integral equations on open curves: Analytical framework and Numerical results
Numerical Analysis
2019-12-03 v3 Numerical Analysis
Analysis of PDEs
Abstract
The Helmholtz wave scattering problem by screens in 2D can be recast into first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introduce two new preconditioners, in the form of square-roots of local operators respectively for the corresponding problems with Dirichlet and Neumann conditions on the arc. They generalize the so-called "analytical" preconditioners available for Lipschitz scatterers. We introduce a functional setting adapted to the singularity of the problem and enabling the analysis of those preconditioners. The efficiency of the method is demonstrated on several numerical examples.
Keywords
Cite
@article{arxiv.1905.13602,
title = {New preconditioners for Laplace and Helmholtz integral equations on open curves: Analytical framework and Numerical results},
author = {François Alouges and Martin Averseng},
journal= {arXiv preprint arXiv:1905.13602},
year = {2019}
}