Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces

This study is devoted to some numerical issues in the boundary integral solution of the scattering of an acoustic wave by an open surface. More precisely, it deals with the construction of a cheap analytical preconditioner to enhance the iterative solving of this kind of equation. Detailed attention is paid to bring out the reasons that make this construction much more difficult than for closed surfaces. This preconditioner is carefully tested and compared to two more usual ones for two and three dimensional problems. It is shown that this preconditioner provides a cheap and efficient tool making reliable the iterative solving. The discussion also precisely brings out the issues where further studies are still needed to improve its efficiency.