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Accuracy of the Yee FDTD Scheme for Normal Incidence of Plane Waves on Dielectric and Magnetic Interfaces
arXiv:2512.14863v1 Announce Type: new
Abstract: This paper analyzes the accuracy of the standard Yee finite-difference time-domain (FDTD) scheme for simulating normal incidence of harmonic plane waves on planar interfaces between lossless, linear, homogeneous, isotropic media. We consider two common FDTD interface models based on different staggered-grid placements of material parameters. For each, we derive discrete analogs of the Fresnel reflection and transmission coefficients by formulating effective boundary conditions that emerge from the Yee update equations. A key insight is that the staggered grid implicitly spreads the material discontinuity over a transition layer of one spatial step, leading to systematic deviations from exact theory. We quantify these errors via a transition-layer model and provide (i) qualitative criteria predicting the direction and nature of deviations, and (ii) rigorous error estimates for both weak and strong impedance contrasts. Finally, we examine the role of the Courant number in modulating these errors, revealing conditions under which numerical dispersion and interface discretization jointly influence accuracy.
Abstract: This paper analyzes the accuracy of the standard Yee finite-difference time-domain (FDTD) scheme for simulating normal incidence of harmonic plane waves on planar interfaces between lossless, linear, homogeneous, isotropic media. We consider two common FDTD interface models based on different staggered-grid placements of material parameters. For each, we derive discrete analogs of the Fresnel reflection and transmission coefficients by formulating effective boundary conditions that emerge from the Yee update equations. A key insight is that the staggered grid implicitly spreads the material discontinuity over a transition layer of one spatial step, leading to systematic deviations from exact theory. We quantify these errors via a transition-layer model and provide (i) qualitative criteria predicting the direction and nature of deviations, and (ii) rigorous error estimates for both weak and strong impedance contrasts. Finally, we examine the role of the Courant number in modulating these errors, revealing conditions under which numerical dispersion and interface discretization jointly influence accuracy.
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