FCC-FDTD Algorithm In Electromagnetic Field

The traditional FDTD(Finite Difference Time Domain)algorithm based on Yee grids has inevitable problems of numerical dispersion and anisotropy.Since the advent of Yee-FDTD algorithm,there have been many methods to improve numerical dispersion and isotropy,but these methods have more or less some defects and limitations.In recent years,a new kind of grid---Face Centered Cubic(FCC)has been applied to FDTD algorithm,and a new FCC-FDTD algorithm has been constructed.This algorithm has more relaxed stability conditions and better isotropy and has broad application prospects.In this thesis,the discretization of Maxwell's time domain equations on FCC grid,first-order Mur absorption boundary conditions and total field boundary conditions are derived from two dimensions.The correctness of each sub-algorithm of FCC-FDTD is verified by numerical examples.This thesis first introduces the FCC grid,on this basis,the discretization of Maxwell's time domain equations on three-dimensional FCC grid is derived and a new programming method is proposed,which can avoid cumbersome classification discussions and constraints.Then this thesis analyzes the stability conditions and isotropy of the three-dimensional FCC-FDTD algorithm,and draws the conclusion that it has more relaxed stability conditions and better isotropy than the Yee-FDTD algorithm.Then,by simulating the resonant frequency of the rectangular resonant cavity,the correctness of the FCC-FDTD algorithm and the programming method proposed in this thesis are verified.Then this work projects the FCC grid into 2D,and the discrete iteration formula of the 2D FCC-FDTD algorithm is derived.Finally,through numerical examples,it is found that the two-dimensional FCC-FDTD algorithm has a problem that the adjacent field value is not in an order of magnitude and two solutions are proposed.Subsequently,this thesis studies the first-order Mur absorption boundary conditions under the FCC-FDTD algorithm,and derives the first-order Mur absorption boundary discrete iterative formula in the two-dimensional and three-dimensional cases.Through numerical examples,it is found that under two-dimensional conditions,the boundary can correctly absorb electromagnetic waves,but as the calculation proceeds,the algorithm begins to diverge.In order to improve the stability of the algorithm,this thesis puts forward two other discretization methods,so that the stability of the absorption boundary has been effectively improved.Finally,this thesis studies the total field boundary conditions of the FCC-FDTD algorithm,derives the total field boundary conditions in the two-dimensional case,optimizes the total field boundary conditions in the three-dimensional case,avoiding excessive classification discussions.Finally,a numerical example verifies the correctness of the method.