電磁場の数値計算差分法

概要

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Non-standard finite difference methods can be used to solve certain kinds of differential equations exactly in one dimension. In this paper we extend the methodology of non-standard finite differences to two and three dimensions. We introduce a new second- order non-standard finite difference, which when used in the Yee algorithm can improve the solution accuracy by about l0,000 on a course grid, with only a modest increase in computational time, and algorithmic complexity. This algorithm is well suited for parallel computers because the computational molecule is small. There are some limitations, but they can be partially or completely circumvented. In addition the algorithmic stability is higher so that fewer time steps can be used. We have applied our methods to study optical waveguides and Mie scattering. We visualize the computed electromagnetic fields periodically to create movie-like visualizations of wave propagation and scattering processes while the computation is running.
社団法人電子情報通信学会の論文
1996-10-17