Two kinds of computational electromagnetics (CEM) methodology are discussed for the challenges in integrated circuit (IC) and printed circuit board (PCB) design. One is an extension of Cagniard-de Hoop method that provides analytic time-domain expressions for the field constituents, making up some drawbacks of numerical techniques that would lose power in super-high frequency simulation or extreme fine structure. A modeling of line-source excited by electromagnetic pulse is analyzed for a thin sheet with high-contrast dielectric and conductive properties. The response of reflection and transmission to the power exponential pulse and the power exponential monocycle pulse are studied using this newly proposed method consequently as a benchmark for practical design. The other method focuses on improving the broadband accuracy of the mixed-form fast multipole algorithm (MF-FMA) by applying rotation techniques. Coordinate system rotation with rotation matrix and pseudo-spectral projection rotation based on fast Fourier transform (FFT) are discussed. Through rotation, translation matrices become very sparse, which enables us to save storage as well as the CPU time. Either of them has certain advantages depending on the number of harmonics used. Hence, increasing the number of multipoles in the low frequency regime to shift up the transition region of MF-FMA can be feasible to improve the overall accuracy significantly. Numerical results of inter connector and sphere with large number of unknowns are given to certify the effectiveness of rotation methods. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy