Applications of Multi-Resolution Time Domain (MRTD) method to electromagnetic engineering

The finite different time domain (FDTD) method, introduced by K. S. Yee in 1966, is one of the most widely used electromagnetic computational methods. The FDTD method is simple and versatile, but it requires substantial computer resources to model electromagnetic problems, especially for electrically large structures. As an alternative solution to these computational issues, the Multi-Resolution Time Domain (MRTD) method, which was first introduced by Krumpholz and Katehi in 1995, has great potential and is very promising for reducing the grid density close to the Nyquist sampling rate. It has been reported that the MRTD scheme can significantly save computer resources for both computational CPU time and memory capacity.; The objective of this research work is to develop a systematic MRTD scheme for practical applications. A generalized MRTD scheme, which is based on both orthogonal and biorthogonal scaling and high-level resolution wavelet functions, has been developed in this research. The MRTD scheme has been applied in conjunction with an adjustable multiple image technique (MIT) for the truncation of a boundary with a perfectly electric conductor (PEC), and an anisotropic perfectly matched layer (APML) for the truncation on open boundaries. A simplified MRTD scheme using diagonal matrices and transformed diagonal matrices is presented and evaluated. The advantages and disadvantages of the MRTD schemes based on different MRA families are generalized from both theoretical and practical viewpoints.; The MRTD scheme developed in this research, as a generalized Maxwell's solver, is successfully applied to the analysis of a number of practical electromagnetic structures, such as electromagnetic wave propagation in layered spaces, monolithic millimeter-wave integrated circuits (MMICs), and scattering radar cross sections for different targets. In order to express the advantages of the MRTD scheme over the conventional FDTD scheme, the application of the MRTD scheme to electrically large electromagnetic problems, such as wave propagation in optical devices, field distribution inside of car and lecture hall models, is presented. The research is extensively validated for a variety of applications through comparisons with available results that have been published in the literature.