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- Title
Hybrid basis scheme for computing electrostatic fields exterior to close-to-touching discs.
- Authors
CROWDY, D. G.; TANVEER, S.; DELILLO, T.
- 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 twodisc 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.
- Subjects
HYBRID systems; ELECTROSTATIC fields; MATHEMATICAL expansion; SET theory; RADIAL basis functions
- Publication
IMA Journal of Numerical Analysis, 2016, Vol 36, Issue 2, p743
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drv030