Abstract

In layered media, the solution of Maxwell’s equations suffers a strong or weak discontinuity at the layer boundaries. Finite-difference schemes providing convergence on strong discontinuities have been proposed for the first time. These are conservative bicompact two-point schemes with mesh nodes lying on the layer boundaries. A fundamentally new technique for taking into account the medium dispersion is proposed. All these features ensure the second order of accuracy of the schemes on discontinuous solutions. Numerical examples illustrating these results are given.

中文翻译：

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分层介质中麦克斯韦方程组的双紧有限差分格式

摘要

在分层介质中，麦克斯韦方程组的解在层边界处遭受强或弱的不连续性。首次提出了在强不连续点上收敛的有限差分方案。这些是保守的双紧凑两点方案，其网格节点位于层边界上。提出了一种从根本上考虑介质分散的新技术。所有这些功能确保了方案在不连续解上的二阶精度。给出了说明这些结果的数值示例。