BIT Numerical Mathematics

, Volume 52, Issue 3, pp 615–637

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


  • B. Engquist
    • Department of Mathematics and Institute for Computational Engineering and SciencesThe University of Texas at Austin
    • Department of Numerical AnalysisCSC, KTH
  • O. Runborg
    • Department of Numerical AnalysisCSC, KTH
    • Swedish e-Science Research Center (SeRC)

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 L 2 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