We consider a class of potential problems on a periodic half-space for the modeling of electrified oil films, which are used in the development of novel switchable liquid optical devices (diffraction gratings). A boundary integral formulation which reduces the problem to the study of the oil-air interface alone is derived and solved in a highly efficient manner using the Nyström method. The oil films encountered experimentally are typically very thin and thus an interface-only integral

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... ation is important for avoiding the near-singularity problems associated with boundary integral methods for long slender domains. The super-algebraic convergence of the proposed method is discussed and demonstrated via appropriate numerical experiments. 2010 AMS Mathematics subject classification. Primary 35J05, 45B05, 65N38, 65R20.