二维平面分层媒质中的数值模式匹配算子矩阵理论及计算方法的应用
THE NUMERICAL MODE MATCHING METHOD ON 2-D STRATIFIED MEDIA-MATRIX THEORY AND COMPUTATION METHOD FOR APPLICATION
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摘要: 本文在直角坐标系中针对任意二维非均匀媒质中的电磁场问题,研究并推广了数值模式匹配的算子矩阵理论。提出了更为一般和实用的公式表达,导出了统一的任意激励源展开公式。所导出的公式更便于边界的匹配得到快收敛的数值解答,并且可普遍适用于未正交归一化的基函数和特征函数以及存在简并模式的情况。另外,文中还着重讨论了建立在以上理论基础上的一般数值计算方法。论述了选择分域三角基的优越性。讨论了确定格点的原则,给出了格点坐标的公式,介绍了数值模式匹配法在电磁波传播测井(EPT)中的应用及其数值计算的实现途径;比较了用不同途径的计算结果。所得数值结果与文献报道一致。Abstract: By studying the arbitrary two dimensional problems of EMF in Cartesian coordinates with the numerical mode matching method, this paper presents a series of more general and applicable formulation, including the unified matrix expanding formula suitable for any source excitation. In discussing the computation method, triangular bases are chosen and its advantages are pointed out. A formula of determining grid points is prsented. As an example, a typical problem in the Electromagnetic Propagation Tool (EPT) is solved in different ways by using the proposed theory and methods. The present results agree with the ones in the literature.
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