Recent progress in numerical methods for wave scattering in 3D from doubly-periodic structures.

Alex Barnett

Dartmouth College

We construct a new class of high-order accurate integral equation solvers for the scattering of time-harmonic scalar waves from a doubly-periodic array of smooth obstacles, or a surface with a doubly-periodic array of bumps. This combines recent QBX surface quadratures with a simple quasi-periodizing scheme based on matching on unit cell walls. No quasi-periodic Green's function nor lattice sums are needed; the solver is thus robust for all scattering parameters including Wood's anomalies.

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