Accuracy of Difference Schemes in Electromagnetic Applications: A Trefftz Analysis

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.

Automated summary

The article examines local approximation errors of finite-difference schemes in electromagnetic analysis and proposes two novel methods for comparison. It concludes that a loss of accuracy for Yee-like schemes at slanted material boundaries is unavoidable.