An Enhanced Finite Difference Time Domain Method for Two Dimensional Maxwell's Equations
Numerical Methods for Partial Differential Equations
An enhanced finite-difference time-domain (FDTD)algorithm is built to solve the transverse electrictwo-dimensional Maxwell’s equations with inhomogeneousdielectric media where the electric fields are discontinuousacross the dielectric interface. The new algorithm is derivedbased upon the integral version of the Maxwell’s equationsas well as the relationship between the electric fields acrossthe interface. To resolve the instability issue of Yee’s scheme(staircasing) caused by discontinuous permittivity across theinterface, our algorithm revises the permittivities and makessome corrections to the scheme for the cells around the inter-face. It is also an improvement over the contour-path effectivepermittivity algorithm by including some extra terms in theformulas. The scheme is validated in solving the scatteringof a dielectric cylinder with exact solution from Mie theoryand is then compared with the above contour-path method,the usual staircasing and the volume-average method. Thenumerical results demonstrate that the new algorithm hasachieved significant improvement in accuracy over othermethods. Furthermore, the algorithm has a simple structureand can be merged into current FDTD software packageseasily. The C++source code for this paper is provided assupporting information for public access.
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Meagher, T., Jiang, B., & Jiang, P. (2020). An enhanced finite difference time domain method for two dimensional Maxwell's equations. Numerical Methods for Partial Differential Equations.