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arXiv · 1409.4608

Boundary integral solution of potential problems arising in the modelling of electrified oil films

David J. Chappell
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Abstract

We consider a class of potential problems on a periodic half-space for the modelling 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 Nystr\"{o}m method. The oil films encountered experimentally are typically very thin and thus an interface-only integral representation is important for avoiding the near-singularity problems associated with boundary integral methods for long slender domains. The super-algebraic convergence of the proposed methods is discussed and demonstrated via appropriate numerical experiments.

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David J. Chappell. 2014-09-16. Boundary integral solution of potential problems arising in the modelling of electrified oil films. https://arxiv.org/abs/1409.4608

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