2019/05/31 by Alouges, François, Averseng, Martin
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1905.13602
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.