BIT Numerical Mathematics

, Volume 52, Issue 3, pp 615-637

First online:

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

  • B. EngquistAffiliated withDepartment of Mathematics and Institute for Computational Engineering and Sciences, The University of Texas at Austin
  • , J. HäggbladAffiliated withDepartment of Numerical Analysis, CSC, KTH Email author 
  • , O. RunborgAffiliated withDepartment of Numerical Analysis, CSC, KTHSwedish e-Science Research Center (SeRC)

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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