Rapidly convergent quasi-periodic Green function throughout the spectrum—including Wood anomalies

This work deals with the scattering of acoustic waves from one dimensional rough surfaces. We build a second kind integral equation that works at the Wood anomalies and is numerically efficient. The main idea is the use of a new periodic green function that quickly converges both at the Wood anomalies and away from them. We prove some theoretical results of well-posedness and we show numerical experiments that confirm the relevance of our method.