Quasi-periodic-scattering-problems

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  A new method for periodic scattering problems using 2nd kind boundary integral equations and the free-space Green s function, adding extra degrees of freedom on the unit cell walls, and imposing quasi-periodicity in an expanded linear system.(A new method for periodic scattering problems using 2nd kind boundary integral equations and the free-space Green s function, adding extra degrees of freedom on the unit cell walls, and imposing quasi-periodicity in an expanded linear system. This avoids the problems with the standard approach, namely: the quasi-periodic Green s function is slow to evaluate, it diverges at Wood s anomalies, and it does not handle large aspect ratios well. Our new approach cures all three issues, and can easily be `wrapped around an existing code (e.g. fast-multipole acceleration) for the isolated-obstacle scattering problem. It includes the latest talk slides: "A new integral representation for quasi-periodic scattering problems in two dimensions")