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arXiv · 1409.2466

Hybrid Basis Scheme for computing Electrostatic fields exterior to close-to-touching discs

D. G. Crowdy·S. Tanveer·T. Delillo
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Abstract

This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-cylinder case. The key idea is to represent the required complex potential using a hybrid set of basis functions comprising the usual Fourier-Laurent expansion about each circle centre comple- mented by a subsidiary expansion in a variable associated with conformal mapping of the physical domain to a concentric annulus domain. We also rigorously prove that there is a representation of the solution in the hybrid basis with faster decay rate of coefficients than is obtained by using a non-hybrid basis, thereby providing a rationalization for the success of the method. The numerical scheme is easy to implement and adaptable to the case of multiple close-to-touching cylinders.

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D. G. Crowdy, S. Tanveer, T. Delillo. 2014-09-08. Hybrid Basis Scheme for computing Electrostatic fields exterior to close-to-touching discs. https://arxiv.org/abs/1409.2466

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