Improving the Accuracy of FDTD Approximations to Tangential Components of the Coupled Electric and Magnetic Fields at a Material Interface

The finite-difference time-domain (FDTD) method is one of the most popular tools used for modeling important electromagnetic wave propagation and scattering problems. Of the many variations on the basic formulation, conventional orthogonal schemes remain prevalent because of their high level of accuracy and relative ease of implementation. Inaccuracies do persist, however, and in this paper a simple, computationally efficient remedy to an error that occurs when simulating waves that impinge on a material interface is identified. The detail of when and how the error occurs is illustrated using a simplistic interface scenario, with an analytic electric field being used to drive a single FDTD magnetic field update step. The resulting FDTD approximations are compared to the analytic solution to reveal the extent of the error. The proposed modification is then introduced and its remedial effect shown by repeating the above comparison using the modified FDTD equations. The broader effects of the proposed modification are demonstrated using a practical, 3D, full-wave FDTD forward modeling tool, taking scenario examples from the application area of ground penetrating radar (GPR). It is concluded that the overall accuracy of conventional, orthogonal FDTD schemes is improved, without unduly increasing their computational burden or algorithmic complexity.