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

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Abstract

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.

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Notes

  1. Note that TE will never refer to the transverse electric field from here on.

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Authors and Affiliations

  1. Department of Mathematics and Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C1200, Austin, TX, 78712, USA

    B. Engquist

  2. Department of Numerical Analysis, CSC, KTH, 100 44, Stockholm, Sweden

    J. Häggblad & O. Runborg

  3. Swedish e-Science Research Center (SeRC), KTH, 100 44, Stockholm, Sweden

    O. Runborg

Authors
  1. B. Engquist
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  2. J. Häggblad
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  3. O. Runborg
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Correspondence to J. Häggblad.

Additional information

Communicated by Jan Hesthaven.

Engquist’s research was partially supported by the NSF grants DMS-0714612 and DMS-1016577. Häggblad’s research was supported by the CIAM project of the Swedish Foundation for Strategic Research. Runborg’s research was partially supported by Swedish e-Science Research Center.

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Engquist, B., Häggblad, J. & Runborg, O. On energy preserving consistent boundary conditions for the Yee scheme in 2D. Bit Numer Math 52, 615–637 (2012). https://doi.org/10.1007/s10543-012-0376-2

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