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

• Published in: BIT (Nordisk Tidskrift for Informationsbehandling) Vol. 52; no. 3; pp. 615 - 637
• Main Authors: Engquist, B., Häggblad, J., Runborg, O.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-09-2012; Springer
• Subjects: Computational electromagnetics; Computational Mathematics and Numerical Analysis; Exact sciences and technology; FDTD; Mathematics; Mathematics and Statistics; Numeric Computing; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Yee scheme; 35L05; Computational electromagnetics; Yee scheme; 78M20; 65M12; FDTD; Approximation; Finite volume method; Boundary condition; Numerical analysis; Wave propagation; Computer architecture; Two-dimensional calculations
• ISSN: 0006-3835; 1572-9125; 1572-9125
• 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.