Higher-Order Time-Domain Computational Electromagnetic Methods

Computational electromagnetics has been an important research area because of its capability to accurately and flexibly model and simulate what is really occurring in electrical circuits and electromagnetic systems. In particular, the demands for efficient analysis of broadband signal excitation have driven the development of time-domain techniques. The requirement for the conventional time-domain techniques, however, that can not accurately simulate wave propagation over many periods of time suggests that high-order time-domain techniques should be considered. On the other hand, the accurately model for the geometric complexity also requires the further development of the conventional time-domain techniques. According to the problems above, the high-order accurate time-domain techniques have been deeply studied in this paper. The work of author mainly focuses on:1. The two-dimensional embedded boundary finite-difference time-domain algorithm (FDTD) is studied in detail in order to realize accurate model for curve boundary and interface, which is impossible for conventional FDTD algorithm. The proper modification about two-dimensional embedded boundary FDTD algorithm is made in the case of curve PEC boundary.2. The Fourier pesudospectral time-domain (FPSTD) algorithm is studied in detail and its dispersion relation and stability condition are derived. Based on it, the combination between FPSTD algorithm and conventional FDTD algorithm is extended into the combination between FPSTD algorithm and arbitrary-order FDTD algorithm, and dispersion relation and stability condition of new algorithm are analyzed.3. The multidomain Chebyshev pseudospectral time-domain (MCPSTD) algorithm is deeply discussed. On the basis of the systematical analyses of its domain mapping technique and patching condition and well-posed perfectly matched layer formula, the MCPSTD algorithm is used to solve two-dimensional and 2.5 dimensional and three-dimensional electromagnetic problems.4. The implicit and explicit time integration schemes are used to improve the stability condition of the MCPSTD algorithm. In implicit time integration, the combination between ADI technique and the MCPSTD algorithm is used to improve the stability condition and efficiency;in the explicit time integration, Super-Time-Stepping method is used to accelerate explicit time integrationscheme so that the stability condition and efficiency are improved.5. In cylindrical and spherical coordinates, the multidomain pseudospectral time-domain (MPSTD) algorithm is presented in order to improve the corresponding algorithm in Cartesian coordinate for the accurate and efficient time-domain computation of scattering by bodies of revolution (BOR). Unsplit-field well-posed PML formula in cylindrical and spherical coordinates are derived, and the Fourier collocation method is utilized in the azimuthal direction and the Chebyshev collocation method in others directions so that the MPSTD algorithm can utilize symmetry of BOR.6. Beginning with one-dimensional and two-dimensional and three dimensional electromagnetic problems, the discontinuous Galerkin method (DGM) is deeply studied in order to improve the limitations inherent in conventional spectral methods for model for the complex geometries. Based on systematical description of its element mapping technique and implementation of Galerkin method and boundary condition between elements, the well-posed PML formula are applied into DGM in order to simulate the infinite computational domain.7. The full-wave simulations of double negative (DNG) medium are made using higher-order time-domain computational electromagnetic methods. Based on complex coordinate stretching technique, the PML formula applied for Lorentz medium and DNG medium are developed, respectively. According to the formula above, MCPSTD algorithm and DGM are used to analyze unusual EM phenomena in DNG medium.