Novel fast algorithms for time domain integral equation analysis of antennas and circuits

Present-day numerical solvers for analyzing electromagnetic transients rely on either differential- or integral-equation-based methods. Traditionally, differential-equation-based methods have been preferred over their integral equation counterparts, which historically have been perceived as computationally expensive. Recently, a host of plane wave time domain (PWTD) algorithms have been developed; the PWTD-augmented time domain integral equation (TDIE) solvers accomplish for the time domain wave equation (and related Maxwell's equations) what fast multipole methods previously achieved for the Poisson and Helmholtz equations, viz., a significant reduction in computational cost associated with the analysis of large-scale problems. Previously, PWTD-augmented TDIE algorithms have been applied to the analysis of acoustic and electromagnetic scattering from large three-dimensional surface structures.; This dissertation focuses on the development of state-of-the-art TDIE-based methods for analyzing electromagnetic transients in broadband antenna systems and circuits. This is achieved by (i) constructing efficient marching-on-in-time solvers suitable for analysis of scattering and radiation from perfect electrically conducting surface-wire and penetrable dielectric structures, (ii) tailoring the currently existing PWTD schemes to complement these solvers, (iii) extending the PWTD technology for fast analysis of structures with highly varying length scales, and (iv) applying the resulting algorithms to the analysis of nonlinear devices and systems by developing a hybrid circuit-electromagnetic solver. The proposed effort expands the applicability of PWTD-augmented TDIE solvers to the realm of electromagnetic compatibility and electromagnetic interference analysis of electronic and electromagnetic circuits.