WINDOWED GREEN FUNCTION METHOD FOR WAVE SCATTERING BY PERIODIC ARRAYS OF 2D OBSTACLES

We present a novel Boundary Integral Equation (BIE) method designed for solving planewave scattering problems involving periodic line arrays of two-dimensional penetrable obstacles. Our approach employs a direct BIE formulation over the unit cell, that leverages the simplicity of the free-space Green function. Integrals over the unbounded unit-cell boundaries are approximated using the Window Green Function (WGF) method. Coupled with a finite-rank op- erator correction to enforce the Rayleigh radia- tion condition, this yields a robust second-kind BIE system that produces convergent solutions even at challenging Rayleigh-Wood anomalies. The corrected windowed BIE can be discretized using standard Nyström and boundary element methods, resulting in linear systems suitable for iterative solvers and fast matrix-vector product algorithms.