Research Of FDTD Algorithm Based On Face-centred Cubic(FCC)Grids

Since finite difference time domain(FDTD)method has been developed,it has been more and more widely applied,because of its simple description,easily understood,and intuitively describing the electromagnetic problem at the time domain in the process of electromagnetic simulation.At present,the computer technologies rapidly developing FDTD algorithm has become a mature and efficient numerical method with higher efficiency and precision.However,the conventional computing grid is Yee cell,and it can lead to anisotropy to reduce calculation accuracy.In this paper,we focus on a new computational grid——face-centred cubic(FCC)grids.Compared with Yee cells,FCC grid has better isotropic effect and more relaxed stability condition,and higher calculation accuracy.In this paper,it has given the equations of the FDTD method based on FCC grid,and utilized this method to calculate the two rectangular resonators which are respectively filled with air and plasma to obtain the relevant conclusions.At the same time,it is important to research the connection boundary conditions of FDTD method based on FCC grid.And there is an example to validate the correctness of this condition.Firstly,this paper summarizes the origin of the FCC grid and its development at home and abroad,and introduces the structure of the FCC grid in detail,and then gives the spatial position vector relationship between the electric field and the magnetic field in the FCC grid.At the same time,the discrete iterative relationship formulas between the electric field and the magnetic field have been deduced in the general medium based on the FCC grid.The stability conditions of FDTD method based on FCC grid are analyzed in detail,and compared with ones of FDTD method based on Yee cell.What's more,in order to verify the correctness of the formulas,this article gives an example that is simulating the resonant frequency to obtain the resonant frequency of 111 TM in the general medium,compared with the results of Yee cell in the same condition.And the results show that the FDTD method based on FCC grid is correct and has higher calculation accuracy.Then,the FCC grid is applied to the plasma medium to get the relationship formulas between the electric field,the magnetic field and the current density from the Maxwell equations.And the iterations of the current density are deduced by convolution algorithm and Laplace transformation method from the constitutive equation.At the same time,in order to verify the correctness of the plasma meshing method based on the FCC grid,this paper utilizes the mode coupling method to calculate a resonant cavity filled with non-time-varying plasma.The results meet the mode coupling method,indicating that the method is correct.Finally,in order to better apply this method to scattering calculation,this paper also research the connection boundary condition of the FDTD method based on FCC grid.Firstly,the discrete iterative relationship equations of the electric field and the magnetic field which show how to join the incident wave are given around connection boundary in the paper.And then,the spatial amplitude distribution of the sinusoidal field in the whole calculation region is analyzed to verify the correctness of connection boundary condition in the FDTD method based on the FCC grid.These research results of paper can provide feasible algorithms for analyzing the targets which filled with complicated mediums in the future.