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FALL 2015 Boundary integral solution of potential problems arising in the modelling of electrified oil films
David J. Chappell
J. Integral Equations Applications 27(3): 407-430 (FALL 2015). DOI: 10.1216/JIE-2015-27-3-407

Abstract

We consider a class of potential problems on a periodic half-spacefor the modeling of electrified oil films, which are used in thedevelopment of novel switchable liquid optical devices (diffractiongratings). A boundary integral formulation which reduces the problemto the study of the oil-air interface alone is derived and solved ina 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 method is discussed and demonstrated via appropriate numerical experiments.

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David J. Chappell. "Boundary integral solution of potential problems arising in the modelling of electrified oil films." J. Integral Equations Applications 27 (3) 407 - 430, FALL 2015. https://doi.org/10.1216/JIE-2015-27-3-407

Information

Published: FALL 2015
First available in Project Euclid: 17 December 2015

zbMATH: 1333.35182
MathSciNet: MR3435807
Digital Object Identifier: 10.1216/JIE-2015-27-3-407

Subjects:
Primary: 35J05, 45B05, 65N38, 65R20

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.27 • No. 3 • FALL 2015
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