The article examines local approximation errors of finite-difference schemes in electromagnetic analysis. Despite a long history of the subject, several accuracy-related issues have been overlooked and/or remain controversial. For example, conflicting claims have been made in the literature about the order of Yee-like schemes in the vicinity of slanted or curved material interfaces. Two novel practical methods for comparison of local accuracy of difference schemes are proposed: one makes use of Trefftz test matrices , and the other one relies on a new measure of approximation accuracy in scheme-exact Trefftz subspaces . One particular conclusion is that a loss of accuracy for Yee-like schemes at slanted material boundaries is unavoidable.

中文翻译：

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电磁应用中差分方案的精度：Trefftz分析

本文考察 当地的电磁分析中有限差分格式的近似误差 尽管该主题已有很长的历史，但一些与准确性相关的问题已被忽略和/或仍是有争议的。例如，关于倾斜或弯曲的材料界面附近的类似Yee的方案的顺序，在文献中已经提出了相互矛盾的主张。提出了两种新颖的比较差分方案局部精度的实用方法：一种利用Trefftz测试矩阵 ，而另一种则依赖于一种新的近似精度度量 方案精确的Trefftz子空间 。一个特别的结论是，不可避免地会在倾斜的材料边界处损失类似Yee的方案的准确性。