A Subgridding Scheme With The Unconditionally Stable Explicit FDTD Method

The recent dramatic advances in electronic technology have seen the surge of many electromagnetic problems and issues. In particular, electronic environment becomes more and more complex, which in turn makes electromagnetic phenomena more and more prominent. Among various computational methods for analyzing the electromagnetic problems, the finite-difference time-domain(FDTD) is a simple and effective method. However, when it is applied to solve fine or small structures, subgridding schemes are often used but they encounter the problem of solution instability. In order to solve it, this paper studied the solution with the explicit unconditionally stable FDTD method.This thesis presents the research on the traditional FDTD method, derivation of its basic equations, analysis of the absorbing boundary, and description of the stability and the numerical dispersion. In FDTD method, the time step and space cell must satisfy the Courant Friedrich Levy(CFL) condition in order to maintain FDTD solution stability. To deal with the problem, an explict FDTD unconditional stable FDTD method is developed by first identifying the stable and unstable modes in the FDTD solutions and then filtering out the unstable modes.Then in the FDTD subgriding, we use the wave equation subgridding method and then propose a hybrid FDTD method based on the explict unconditionally stable FDTD method. The latter does not require the interpolation in time but in space only. Finally, we make the comparisons between them.