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- W3043433981 abstract "Abstract A new paradigm for cylindrically symmetric electrostatics is presented and is composed of two parts: the first is a discussion of the two methods of algorithm creation which will demonstrate the single point precisional increase obtained by using algorithms of high orders and the second will provide a solution to boundary value problems introduced by these algorithms. The precision of new paradigm is illustrated by trajectory calculations through two spectrometer type devices, the hemisphere deflector analyzer (HDA) and the spherical deflector analyzer (SDA). The model is suitable for solving general curvilinear geometries by FDM using algorithm orders 2 through 10. By using order 2, 4, and 10 algorithms, trajectories have been simulated, their end position determined and the resulting precisions reported both with and without the use of multi regions. It was found that multi regions, while improving the precision of the order 4 algorithm by ∼1 order of magnitude had no effect on the precisions of the order 2 algorithm but improved the order 10 algorithm by ∼5 orders of magnitude. As a result, the order 10 algorithm with multi regions obtains trajectory end point precision levels from ∼ 10 − 11 to 10 − 13 . Thus the “new paradigm”, while retaining the simplicity of classic FDM, has the promise of markedly improving precision levels in electrostatic calculations." @default.
- W3043433981 created "2020-07-23" @default.
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- W3043433981 date "2020-01-01" @default.
- W3043433981 modified "2023-09-25" @default.
- W3043433981 title "A new paradigm for FDM: cylindrically symmetric electrostatics" @default.
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- W3043433981 doi "https://doi.org/10.1016/bs.aiep.2020.06.005" @default.
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