Developed Algorithms Of FDTD Method And The Achievements For Perfect Conductor Boundary

Computational electromagnetics is a production that combines electromagnetic theory together with mathematics and computer technology, which is developing to the goals of high precision, high performance and high speed rapidly. Many difficult electromagnetic problems that are unable to be solved in the previous can find good solutions and obtain accurate results. More and more difficult electromagnetic problems have been appearing in actual project, which promotes computational electromagnetics to a higher level. Based on Maxwell’s equations, the solutions obtained from analytical methods and numerical methods are the main issues of computational electromagnetics. Generally only classical electromagnetic problems have analytical solutions, while numerical methods have become chief means, sometimes the only means, to solve difficult problems.As a classical full wave analysis method, FDTD method have wide range of applications, which is one of the most interested and the most rapidly developing numerical methods in recent years. Maxwell’s equations are the basic equations to descript electromagnetic phenomena. According to the curl equations, in the other words differential forms, of Maxwell’s equations, FDTD method takes central difference approximation to the first order partial derivative of time and space, and then is converted to displayed differential operation, thus the continuous electromagnetic field values are discrete sampled both in time and space. FDTD method can describe the propagation characteristics of the time domain electromagnetic field. For a given problem, if the initial conditions and boundary conditions are known, we can obtain electromagnetic field distribution on each time step and space step by FDTD method recursive iterations. With the development of computer hardware conditions, innovative researches associated with FDTD method have been emerging. It is believed in the near future that FDTD method will be interested by more and more researchers in computational electromagnetics. However, FDTD method also has its own shortcomings that can not be ignored. On the one hand, in the approximate solving Maxwell’s equations progress by differential method, numerical dispersion is caused in computing network, and the relationship can be changed by propagation direction of numerical wave mode and different levels of discretization. Therefore FDTD method is restricted by numerical dispersion conditions, that is why space step is not more than 1/10 wavelength. If the obstacle has a larger electrical size, dramatic increase in memory requirements will be resulted in. On the other hand, the time step and the space step of TDTD are not independent, and the time discrete is limited by Courant-Friedrich-Levy (CFL) stable condition, which causes that time step must be changed with space step. In order to achieve convergence, if space step becomes smaller, time iteration steps need adding. Therefore at present for an ordinary PC, FDTD method has shortcomings in the aspect of computational efficiency. For the computational efficiency problem of electromagnetic numerical methods, some developed algorithms have come out in resent years, for example R-FDTD method, ADI-FDTD method, LOD-FDTD method, etc. Actually there are more or less problems to these algorithms in practical applications. In order to achieve more efficient and more accurate numerical solutions, further studies about the developed algorithm of FDTD method have significant importance both in theory and in application.Firstly the research background is elaborated in this paper, containing progress of computational electromagnetics, necessity of developing time domain numerical and introduction to FDTD method. The developed algorithms involved in this paper include R-FDTD method, ADI-FDTD method and LOD-FDTD method. These algorithms can deal with the problems of large storage requirement and long calculating time. Present situations of these developed FDTD method are introduced. In the end the main work in the paper is explained.For calculation models with symmetric characteristic, symmetry boundary conditions truncated by PEC boundary and PMC boundary are systematically analyzed, based on which symmetric truncation method is proposed. Therefore the field values beyond truncation boundaries can be obtained, so as to achieve the FDTD method calculation on truncation boundaries. Feasibility and correctness of symmetric truncation FDTD method are verified by numerical solutions.The necessity for calculating the boundary value of temporary field components in R-FDTD method is presented. It is demonstrated that the 3D R-FDTD method to deal with conductor problems which solves the induced charge density is equivalent to traditional FDTD method. The periodic symmetry R-FDTD method that has obvious advantages in both memory requirement and calculating time is proposed, which combines the advantages of R-FDTD method and symmetric truncation method in chapter 2. Comparing to the original FDTD method, the required memory requirement is reduced to 1/6. Because the calculating complexity of each time step iteration is dropped and the number of grids needing calculating is reduced, the total iterative computation time can be substantially reduced. Feasibility and correctness are verified by numerical solutions.To obtain the Coefficients of the unknown field components of PEC boundary and PMC boundary by accurately solving ADI-FDTD method, the corresponding correction factors are derived by using the perfect conductor boundary conditions before obtaining the coefficients. The bistatic RCS of a single metal cube and two symmetric metal cubes are computed respectively. To be concluded that, the results obtained by using correction factor are well coincided with that of FDTD method by taking perfect conductor boundary as ideal conductor surface, as well as the results obtained by using correction factor are well coincided with that of ADI-FDTD method by taking perfect conductor boundary as symmetry plane of truncated computing space, which are consistent with theoretical conclusions, as well as analysis solutions.It is demonstrated that coefficients of the unknown field components by LOD-FDTD method achieving PEC boundary and PMC boundary are different from the coefficients of traditional LOD-FDTD method. Applying perfect conductor boundary conditions before obtaining the coefficients, the corresponding correction factors are achieved. For the different conditions of taking perfect conductor boundary as ideal conductor surface and symmetric surface of truncated computing space, the difference between corrected coefficients and traditional LOD-FDTD method coefficients is discussed. Preparing to traditional LOD-FDTD method, the corrected coefficients LOD-FDTD method having unified expression can achieve a smaller error when calculating perfect conductor surface, and then numerical verification is taken.