Symplectic time integration methods for retarded potential integral equations

The numerical accuracy and energy conservation are of great importance in real-life electromagnetic (EM) problems, such as tracing the influence of excited wake fields inside accelerator structures on moving charge particles over long time periods. In practice, the essential property needed for accurate time-domain simulations is the fulfillment of the energy conservation law implied by Maxwell equations. Time- domain integral equations (TDIE) are commonly solved by the marching-on-in-time (MOT) or marching-on-in-degree (MOD) methods.