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The present research study mainly involves a survey of diverse timedomain boundary element methods that can be used to numerically solve the retarded potential integral equations. The aim is to address the latetime stability, accuracy, and computational complexity concerns in timedomain surface integral equation approaches. The study generally targets the transient electromagnetic scattering of three dimensional perfectly conducting bodies. Efficient algorithms are developed to numerically solve the electric, magnetic, and combined field integral equations for the unknown induced surface current. The algorithms are mainly categorized into three major discretization schemes, namely the marchingon intime, the marchingoninorder, and the convolution quadrature methods or finite difference delay modeling. Possible choices of spacetime integration are examined and the results are compared with the finite integration techniques solution. The outcome is applied to the non dispersive modeling of the field propagation in particle accelerator structures, when travelling bunches of charged particles passes through the beam line elements.
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