Numerical Analysis Of Finite-Difference Time-Domain And Time-Domain Finite-Element Methods In Electromagnetic Simulation

The research of this dissertation is focus on the Finite-Difference Time-Domain (FDTD) Method and Time-Domain Finite-Element Method (TDFEM).A novel microstrip circulator with a magnetized ferrite sphere for millimeter wave communications is analyzed. The electromagnetic fields inside the ferrite junction are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. A three-dimensional FDTD method for the analysis of this ferrite sphere based microstrip circulator is presented.The Modified Matrix Pencil (MMP) method and the Least-Squares Support Vector Machines (LS-SVM) technique are used in the FDTD method to eliminate the late time instability of time domain responses and extrapolate the time domain responses. The Particle Swarm Optimization (PSO) method is used to optimize the hyperparameterγ,σof the LS-SVM algorithm, which should be tried again and again randomly. By modeling the novel microstrip circulator, some of the instabilities that arise in late times in the time domain are eliminated.The application of FDTD algorithm combined with the short-open calibration (SOC) technique to three-dimensional microstrip discontinuity is firstly studied. This SOC technique is directly accommodated in the FDTD algorithm. It is used to remove the unwanted parasitic errors brought by the approximation of the impressed voltage sources and the feed lines. This new method is used to analyze microstrip discontinuities and finite periodic structures. The scattering parameters of the whole periodic structure can be approximately obtained through analyzing only one cell of it.The conventional FDTD method is limited by the Courant-Friedrich-Levy (CFL) condition while the unconditionally stable alternating-direction-implicit FDTD (ADI-FDTD) method has worse accuracy with the increase of the time step size. The iterative alternating-direction-implicit FDTD (Iterative ADI-FDTD) method is reseached here. This method is exactly the same as the original Crank-Nicolson (CN) method while recognizing the ADI-FDTD method as a special case of a more generalized iterative approach to solve the CN-FDTD method, which can reduce the splitting error of the ADI-FDTD method and no matrix need to be solved. Numerical results demonstrate that this 3D iterative ADI-FDTD method can improve the accuracy of the ADI-FDTD method by using the time step size greatly exceeding the CFL limit within several iterations. The TDFEM method, which solves the second-order vector wave equations using Galerkin's method, is studied. Compared to FDTD, TDFEM can easily handle both complex geometry and inhomogeneous media by using tetrahedral edge elements. Edge basis function and its hierarchical vector basis functions are used while perfectly matched layers (PML) are used to terminate the waves when simulating different structures of cavity, waveguides and microstrips. Several preconditioning techniques, such as Jacobi,SSOR ILU0 and SAI-SSOR, are used to accelerate the convergence of iterative methods, such as CG and GMRES, which are used to solve the large system of linear equations resulted from TDFEM. Convergence properties and the time used of these conventional preconditioning techniques are compared and analyzed. Also the reversing Cuthill-McKee (RCM) ordering method is used to reorder the sparse matrices created by the hierarchical implicit TDFEM scheme in order to makes SAI-SSOR-CG method more efficient.Not only to solve the starecasing limitation but also to avoid solving large sparse matrix, a new domain-decomposition TDFEM method (DDM TDFEM) is researched for numerical simulation of electromagnetic phenomena. The method divides the computation domain into several non-overlapping subdomains and computes both the electric and magnetic fields in each subdomain using the sparse direct solver solving second-order vector wave equations. Similar to FDTD method, a leapfrog-like scheme is employed in the time marching to update the alternating electric and magnetic fields. The system matrix for each subdomain is pre-factorized and stored before time marching, so the subdomain problems are solved efficiently using the local pre-factorized matrices at each time step. It could save much time compared to TDFEM method and could analyze big problems. It also has advantages compared to the comformal mapping CN-FDTD method.