Journal of Integral Equations and Applications

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

David J. Chappell

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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 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.

Article information

J. Integral Equations Applications, Volume 27, Number 3 (2015), 407-430.

First available in Project Euclid: 17 December 2015

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Zentralblatt MATH identifier

Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 45B05: Fredholm integral equations 65N38: Boundary element methods 65R20: Integral equations

Boundary integral method transmission problems Laplace equation Nyström method dielectrophoresis


Chappell, David J. Boundary integral solution of potential problems arising in the modelling of electrified oil films. J. Integral Equations Applications 27 (2015), no. 3, 407--430. doi:10.1216/JIE-2015-27-3-407.

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