This dissertation contains two subjects: further development of numerical technique for the analysis of magnetically induced subsequent fault (MISFault) in overhead power lines and its implementation into a software upgrade; and first-phase of study on the electromagnetic scattering from objects buried below a random rough surface making use of the multidomain pseudospectral time domain (PSTD) method and Monte-Carlo simulation. An initial electric fault can result in strong magnetic torque on the overhead power line conductors, which will make them swing and may bring them to close proximity or in contact with one another, causing a subsequent fault. In Chapter 2, Computer simulations for the analysis of the subsequent fault in transition spans, which are often required in power line topology, are developed. A dynamic analysis of swing movement of power line conductors subsequent to an initial fault is presented to track the smallest distance between the conductors. In Chapter 3, the simulation is implemented into the upgrade of the MISFault analysis software. Its functions are depicted in details. The MISFault software is being used by Duke Energy Company and is expected to be useful to a utility for eliminating the magnetically induced subsequent faults. The multidomain pseudospectral time domain (PSTD) method has been developed and successfully applied to solve a variety of electromagnetic scattering problems in the past decade. It is a novel algorithm with improvement over traditional FDTD method. In Chapter 4, a multidomain PSTD algorithm is developed to investigate the scattering from a 2-D cylinder in free space. Sample numerical results are presented and validated. Then, the theoretical derivations are extended for the analysis of scattering from 2-D objects buried below a random rough surface
