Study Of Modified FDTD Method Based On Collocated Surface Impedance Boundary Conditions

As an efficient and widely applied electromagnetic simulation technique, the finite-difference time-domain (FDTD) method is often employed for solving electromagnetic problems of complex and inhomogeneous medium. Using FDTD method, the numerical value of the electromagnetic field components at each space position can be obtained easily at any time. The popularity of this method stems from the fact that it is not limited to a specific geometry and it does not restrict the constitutive parameters of a scatterer, excitation source, etc. When we use conventional FDTD method to analysis electromagnetic problem of thin coatings covering on large targets, the computational difficulty will be increased because the structure of the target is complex. On the other hand, the thickness of thin coatings will also have an adverse effect on the numerical calculation. Surface impedance boundary conditions (SIBCs) are introduced into the FDTD method, which let us to ignore the coated targets under consideration from computation space and merely discretize the fields of the surrounding space. In this dissertation, based on collocated first-order surface impedance boundary conditions (SIBCs), FDTD models of lossy dielectric and non-magnetized plasma coatings on conductors are studied systematically, respectively. Next, the electromagnetic scattering characteristics of three-dimensional multi-particle plasma are analyzed, and the nearly perfectly matched layer (NPML) absorbing boundary condition (ABC) is presented for truncating three-dimensional (3-D) anisotropic medium. The innovative achievements of the study are as follows:The collocated SIBCs-FDTD method of lossy dielectric coatings on conductors for vertical polarization (TE) and parallel polarization (TM) plane wave at oblique incidence are developed in one-dimensional situation. Electric and magnetic field components on the interface of the coated conductor in FDTD method is collocated effectively. In contrast to the traditional SIBCs-FDTD implementation which is approximated with the magnetic field component on the boundary located at half-cell distance from the interface and half time step earlier in time, it is seen that the numerical stability and computational accuracy of the proposed technique is effectively improved.Next, on the basis of collocated SIBCs, FDTD models of non-magnetized plasma coatings on metal substrates are proposed. The model extends the previous models to complex dispersive coatings and three-dimensional (3-D) numerical examples will be presented. Utilizing rational approximation of tangent function and inverse Laplace transform, the impedance boundary conditions in the time domain are derived. Then, the associated discrete3-D FDTD expression is obtained using Piecewise Linear Recursive Convolution (PLRC) method. The reflection of TE and TM plane wave at varying oblique incident angles from the plasma coating surfaces is simulated. The results are numerically verified by the comparison with the exact results in the one-dimensional situation. Magnitude and phase error of the calculated reflection coefficients are studied and the convergence properties of the algorithm proposed in the paper is demonstrated. Finally, the radar cross section (RCS) of a perfectly conducting cube covered with plasma coatings is calculated utilizing the proposed collocated SIBC. It is seen that huge computational memory requirements and computation time savings can be realized using the proposed algorithm.Then, the electromagnetic scattering characteristics of three-dimentiosnal multi-particle plasma are analysed. The proposed algorithm is numerically verified, and the influence of electrons, positive ions and negative ions on the radar cross section (RCS) of plasma sphere is considered.Finally, based on the nearly perfectly matched layer (NPML) theory, a finite-difference time-domain (FDTD) absorbing boundary condition (ABC) is presented for truncating three-dimensional (3-D) anisotropic medium. In the proposed technique, the complex coordinate stretching in the NPML scheme and the spatial interpolation method are employed. The associated ABC formulations have the advantage of simplicity in the FDTD implementations. For additional intermediate variables are not needed to introduced, the programming complexity is reduced greatly. The radiation fields and the relative reflection coefficients of an electric dipole in anisotropic media are calculated using the presented ABC. The results are numerically verified by the comparison with the reference solutions. The radiation phase distribution of the time-harmonic field is also simulated with the algorithm, which further shows the high effective absorbing performance of the proposed method.As mentioned above, the modified FDTD method not only offers the effective way to solve the electromagnetic problems of complex targets, but also makes the FDTD method more mature and perfect.