We will describe some new integral formulations for wave scattering problems in quasiperiodic and semi-infinite domains that are well-conditioned, handle complex obstacle shapes and are compatible with fast multipole acceleration. These methods combine ideas from the classical theory of images with Sommerfeld integrals computed by contour deformation. Our methods apply in both two and three dimensions and their efficiency is illustrated with numerical examples. This is joint work with Alex Barnett,
Mike O'Neil and Zydrunas Gimbutas.
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