Abstract

The half-space matching method (HSMM, Bonnet-BenDhia, Fliss, Tonnoir, 2018) is a rather new computational method for general 2D scattering problems that is well-suited to solving canonical scattering problems where the scatterer is a bounded or undounded convex polygon or wedge. In these cases it reduces the scattering problem to the solution of a system of second-kind integral equations on infinite half-lines that are the continuations of the sides of the polygons/wedges into the domain of propagation. The recent complex-scaled version of the HSMM (Bonnet-BenDhia, Chandler-Wilde, Fliss et al, 2022), in the spirit of PML or similar complex-scaling, additionally deforms these half-lines into the complex plane, resulting in a method that is provably well-posed for the most interesting case of real wavenumbers. In this talk we show, via an analysis that is explicit in the wavenumber, that this complex-scaled HSMM is particularly effective for these canonical problems in the high-wavenumber regime. We illustrate the talk by computational results, including for scattering by right-angled wedges.