Unconditionally stable and wavelet based finite-difference time-domain methods for electromagnetic simulations

This dissertation is on developing the finite-difference time-domain (FDTD) numerical method for full-wave time-domain electromagnetic simulations. Yee's formulation of the FDTD method (Yee's FDTD) is a versatile, robust and popular technique for solving the time-dependent Maxwell's equations. Nevertheless, accurate electromagnetic simulations of electrically large structures containing fine detail are required in modern applications of Yee's FDTD. A purpose of this work is improving the FDTD method in solution accuracy, decreasing numerical dispersion and removing restrictions on the time step imposed by the computational stability limit. Conditionally and unconditionally stable FDTD schemes are considered in this dissertation.;A rigorous analysis of unconditional stability for the ADI-FDTD and CNSS-FDTD schemes avoiding use of the von Neumann; spectral criterion is proposed because it has been found that the ADI-FDTD amplification matrix is not normal. It is also shown rigorously that the ADI-FDTD and CLASS-FDTD schemes have identical numerical dispersion in the frame of plane waves.;An eigenvalue based dispersion relation is presented. This relation matches identically referred ones in each particular case, while it provides a general governing equation to estimate 3D numerical dispersion of the conditionally and unconditionally stable FDTD schemes.;The SBTD's spatial discretization is proposed to improve accuracy of the hybrid ADI-FDTD scheme. It is shown that the hybrid ADI-FDTD scheme with the leap-frog SBTD discretization at the coarse part of the computational domain is superior over the ADI-FDTD scheme in terms of solution accuracy and CPU time.;A conditionally stable wavelet-based sampling biorthogonal time-domain (SBTD) scheme is analyzed and compared with other higher order FDTD schemes. It is shown that the SBTD scheme is an effective technique for decreasing numerical dispersion and for improving accuracy of the numerical solution. Further improvement of accuracy is achieved with the proposed combination of SBTD and Yee's FDTD spatial finite-differences in the update equations. Numerical examples are provided.