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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Abstract

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

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

Dates
First available in Project Euclid: 17 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1450388942

Digital Object Identifier
doi:10.1216/JIE-2015-27-3-407

Mathematical Reviews number (MathSciNet)
MR3435807

Zentralblatt MATH identifier
1333.35182

Subjects
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

Keywords
Boundary integral method transmission problems Laplace equation Nyström method dielectrophoresis

Citation

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. https://projecteuclid.org/euclid.jiea/1450388942


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