Hybrid basis scheme for computing electrostatic fields exterior to close-to-touching discs
Crowdy, D. G.
DeLillo, Thomas K.
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D. G. Crowdy, S. Tanveer, and T. Delillo Hybrid basis scheme for computing electrostatic fields exterior to close-to-touching discs IMA J Numer Anal (2016) 36 (2): 743-769 first published online July 1, 2015 doi:10.1093/imanum/drv030
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-disc 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 complemented 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 a faster decay rate of coefficients than is obtained by using a nonhybrid 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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