| This dissertation is concerned with the development of efficient time domain integral equation (TDIE)-based marching-on-in-time (MOT) schemes pertinent to transient analysis of electromagnetic scattering from objects residing in lossy media. Classical MOT schemes have a computational complexity scaling as O( N2sN2t ) and a memory requirement as O( N2sNt ), respectively. To alleviate the demands of computational resources, two techniques are proposed in this dissertation, viz., the Prony series-based recursive convolution scheme and the multilevel plane wave time domain (PWTD) algorithm. The former reduces the computational cost to O( N2sNt log Nt). The latter is the extension of the PWTD scheme for free space and is able to speed up the evaluation of fields radiated by band-limited and time-limited sources far enough away. When these two techniques are hybridized in the MOT scheme, i.e., the recursive convolution scheme evaluates the near-field interaction, and the multilevel PWTD algorithm evaluates the far-field interactions, the enhanced scheme has a computational complexity of O(NsNt log Ns(log Ns + log 2 Nt)) and a memory requirement of O(NsNt). As applications of the developed solver, the electromagnetic scattering from perfect electric conductors residing in lossy media and the light scattering from homogeneous and inhomogeneous biological cells are analyzed. The corresponding TDIEs are also formulated considering the particularities of application scenarios. Numerous numerical examples are presented to demonstrate the fast solver's efficacy and ability to solve realistic problems. |
