Leapfrog ADI-FDTD And Its Applications On Numerical Simulation Of Complex Electromagnetic Structures

Recently, with the development of electronic industry, the problems of electromagnetic research mainly focus on electric large problems and electronic devices in nanoscale. Specifically, with the modern electric war upgrade, the electromagnetic compatibility and interference (EMC/EMI) problems of electric large and multi-scale platforms like aircraft and ship platforms are increasingly important. On the other hand, with the development of semiconductor manufacturing technology, electronic devices are increasingly tend to be small and complex, and the research of electromagnetic environment effects is also increasingly urgent. To solve these problems, one important way is to develop some accurate and efficient numerical computational electromagnetic methods (CEM). Therefore, in this dissertation, the conventional finite-difference time-domain (FDTD) method is further been extended and improved. Specifically, the one-step Leapfrog alternately-direction-implicit FDTD (Leapfrog ADI-FDTD) method has been fully developed for analysis the EMC problems of some Perfect Electric Conducting (PEC) platforms and nanoscale Graphene-based devices. The main academic contributions of this dissertation are summarized as follows:(1) The numerical dispersion of Leapfrog ADI-FDTD method has been analyzed. The unconditionally stable stability of Leapfrog ADI-FDTD method has been proved by three different methods i.e. from analyzing the dispersion equation, time-space eigenvalues, and the eigenvalues of growth matrix. Moreover, different source implementations for the Leapfrog ADI-FDTD method including both current and hard sources are investigated. It is shown that, different from the conventional ADI-FDTD method, the Leapfrog one always possesses asymmetry errors, while the hard source results in larger asymmetry errors than the current source. An optimal current source derived from the conventional ADI-FDTD method is then presented. In addition, it is found that the hard source is less accurate than the current source as the Courant-Friedrich-Levy (CFL) number increases.(2) A new convolutional perfectly matched layer (CPML) is proposed and implemented in one-step Leapfrog ADI-FDTD method. Different from the previous developed PMLs used in the ADI-FDTD methods, the proposed PML has the same form as that used for the conventional FDTD method, requiring only one-step computations of the CPML auxiliary quantities. Stability of the proposed CPML is verified semi-analytically and its high absorption efficiency is proven numerically. The proposed CPML is then applied to a number of applications; they include radiation generated by a current source in free space, propagating and evanescent modes in a rectangular waveguide.(3) Leapfrog ADI-FDTD method including lumped elements is presented. The method is originated from the conventional ADI-FDTD method but without mid time-step computations. Its unconditional stability is analytically proven by combining the von Neumann method with the Jury criterion. In addition, its unconditional stability and high computational efficiency are verified through numerical experiments.(4) An improved Leapfrog ADI-FDTD method is provided for computing surface current distributions of some complex PEC and dielectric composite structures illuminated by an intentional electromagnetic pulse (IEMP). The techniques for introducing into an incident plane wave, updating the iteration equations at the connecting boundaries according to the total and scattered fields (TF/ST), and computing the surface currents are all implemented into the Leapfrog ADI-FDTD algorithm. Some numerical results are given to show the predicted surface current distribution of an aircraft model illuminated by an IEMP with different incident directions and polarizations, and good agreement is obtained in comparison with those of the commercial software CST and FEKO. Moreover, a numerical dispersion optimized Leapfrog ADI-FDTD method is also proposed, where a set of artificial anisotropic parameters is introduced into its implementation. Under such circumstances, its numerical dispersion can be suppressed efficiently. Further, such method is adopted for predicting surface current distributions of some 3-D complex objects illuminated by an electromagnetic pulse (EMP), such as a tank, and good agreement is obtained in comparison with commercial software.(5) The method of surface current distribution calculation is further improved to be used to obtain the complex PEC object in time domain. Moreover, the method of calculated the amplitude and phase of the surface current is also provided. Further, these method are used to simulate the surface current distributions of a PEC Frigate.(6) The Leapfrog ADI-FDTD method is extended and developed for general orthogonal grids. The convolutional perfectly matched layer (CPML) is also derived for general orthogonal grids. The proposed developments are validated and further used for investigation of the earth-ionosphere cavity, with the Schumann resonant frequencies captured. It is numerically demonstrated that the proposed method is unconditionally stable and more efficient than the conventional FDTD method for the problems considered.(7) Leapfrog ADI-FDTD method is proposed for modelling anisotropic magnetized plasma. Further, the method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step Leapfrog ADI-FDTD method.(8) A novel Matrix exponent FDTD method is developed for modeling two-dimensional graphene sheet biased with a magnetostatic field. Moreover, an improved Leapfrog ADI-FDTD method is proposed to study surface plasmon polaritons (SPPs) in optically pumped and electrostatic applied curved graphene structures, with their intraband and interband surface conductivities modelled with the vector fitting technique. Further, the Leapfrog ADI-FDTD method is also developed to analyze the properties of graphene-based frequency selective surface (FSS) and filters.