【講演概要】
低周波の電磁界問題に対して提案されているケルビン変換を電磁波問題に拡張する方法について議論する。ケルビン変換は無限空間を有限空間に写像する座標変換であり，Maxwell 方程式の共形変換とみなすことができる。微分幾何の考え方を用いて，ケルビン外部領域における計量を求め，解析対象領域における計量との比を取ることで，ケルビン変換領域における物質定数の空間依存性が導出される。COMSOLを用いてその考え方を検証した。
【キーワード】
電磁場解析，ケルビン変換，開領域問題，放射電磁場，損失生媒質
【使用製品】
COMSOL Multiphysics, AC/DC, LiveLink for MATLAB
【English title】
Another approach to open-boundary electromagnetic problems.
【Abstract】
Extension of the Kelvin transformation proposed for low-frequency electromagnetic field, to electromagnetic wave problems is studied. The Kelvin transformation is a coordinate transformation that maps an infinite space to a finite space, and can be regarded as a conformal transformation of Maxwell’s equations. By using the concept of differential geometry to obtain the metric in the Kelvin domain and taking the ratio with the metric in the analysis domain, the spatial dependence of the material constants in the Kelvin domain is derived. When dealing with the open boundary problem of the radiated electromagnetic field, the analysis domain is truncated with lossy medium. The loss medium usually needs to be placed at distance of more than a wavelength from the analysis domain. When the typical size of the analysis domain is much smaller than the wavelength, the total analysis domain becomes enormous. By applying the idea of Kelvin transformation and placing the lossy media in the Kelvin domain, it is possible to perform a numerical analysis within a realistic domain size.
【Keyword】
Electromagnetic analysis, Kelvin transformation, Open boundary problem, perfectly matched layer, Semi-infinite ground