BIT Numerical Mathematics

, Volume 52, Issue 3, pp 615–637

On energy preserving consistent boundary conditions for the Yee scheme in 2D


DOI: 10.1007/s10543-012-0376-2

Cite this article as:
Engquist, B., Häggblad, J. & Runborg, O. Bit Numer Math (2012) 52: 615. doi:10.1007/s10543-012-0376-2


The Yee scheme is one of the most popular methods for electromagnetic wave propagation. A main advantage is the structured staggered grid, making it simple and efficient on modern computer architectures. A downside to this is the difficulty in approximating oblique boundaries, having to resort to staircase approximations.

In this paper we present a method to improve the boundary treatment in two dimensions by, starting from a staircase approximation, modifying the coefficients of the update stencil so that we can obtain a consistent approximation while preserving the energy conservation, structure and the optimal CFL-condition of the original Yee scheme. We prove this in L2 and verify it by numerical experiments.


Yee scheme FDTD Computational electromagnetics 

Mathematics Subject Classification (2010)

35L05 65M12 78M20 

Copyright information

© Springer Science + Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  2. 2.Department of Numerical AnalysisCSC, KTHStockholmSweden
  3. 3.Swedish e-Science Research Center (SeRC)StockholmSweden

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