An Enhanced Finite Difference Time Domain Method for Two Dimensional Maxwell's Equations

Document Type

Article

Publication Date

1-23-2020

Publication Title

Numerical Methods for Partial Differential Equations

First page number:

1

Last page number:

16

Abstract

An enhanced finite‐difference time‐domain (FDTD) algorithm is built to solve the transverse electric two‐dimensional Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface. The new algorithm is derived based upon the integral version of the Maxwell's equations as well as the relationship between the electric fields across the interface. To resolve the instability issue of Yee's scheme (staircasing) caused by discontinuous permittivity across the interface, our algorithm revises the permittivities and makes some corrections to the scheme for the cells around the interface. It is also an improvement over the contour‐path effective permittivity algorithm by including some extra terms in the formulas. The scheme is validated in solving the scattering of a dielectric cylinder with exact solution from Mie theory and is then compared with the above contour‐path method, the usual staircasing and the volume‐average method. The numerical results demonstrate that the new algorithm has achieved significant improvement in accuracy over other methods. Furthermore, the algorithm has a simple structure and can be merged into current FDTD software packages easily. The C++ source code for this paper is provided as supporting information for public access.

Keywords

Finite difference time domain; Maxwell’s equations; Second Order convergence; Stability; Effective permittivity

Disciplines

Applied Mathematics | Ordinary Differential Equations and Applied Dynamics

Language

English

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