Some Research On Finite-Difference Time-Domain(FDTD) Method For Electromagnetic Wave

The thesis is mainly about some research on finite-difference time-domain (FDTD) method for electromagnetic wave. There are 4 chapters in all.First, we introduce the object and background of the research: Maxwell equations and some numerical algorithm on them, especially the history and development of FDTD.In chaper 2, we introduce the formulation and cells in the 3-dimension Cart-esian coordinates. Then we investigate the stability and numerical dispersion of the method, including the requirements for the time interval and Courant condition for stability, Besides, we first discuss the aborbing boundary conditions for FDTD from the wave equation, then derive the 1st-order and 2nd-order Mur's absorbing boundary condition. At the end of this chapter we present an efficient boundary condition: perfectly matched layer (PML) for the absorption of electromagnetic wave.Basing on the discrete scheme used in the PML, viz. exponential time-difference (ETD) scheme, the author does some extension and advancement, extending the common exponential difference scheme to 2N-order. In chapter 3, we precisely deduce ETD from the basic differential equation's theory. Then according to the Taylor theorem, we use the linear combinations of the function's values on 2N symmetrical points to approximate the first order partial derivative of spatial variable and get the determinate coefficients. In 3.3, adopting a skillful transformation to convert the ETD into a scheme that is easy to analyse and derive the stability condition, the relation between the order of the scheme and spectrum as well as the order and numerical dispersion. At the end of this chapter, we discuss how to deal with the points which near the boundary and use a numerical example to show the efficiency and effect of the high order method.Chapter 4 is mainly about a creative idea on FDTD, which considering the quantum effect into the computation of the electromagnetic field. The paper investigate the relationship between Maxwell equations and Schrodinger equation, and bring forward the idea to coupled solve them numerically.