On energy preserving consistent boundary conditions for the Yee scheme in 2D
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- Engquist, B., Häggblad, J. & Runborg, O. Bit Numer Math (2012) 52: 615. doi:10.1007/s10543-012-0376-2
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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 L2 and verify it by numerical experiments.