Application of Analytical Retarded-Time Potential Expressions to the Solution of Time Domain Integral Equations

Recently, exact closed-form expressions of the electric and magnetic fields and potentials due to impulsively excited Rao-Wilton-Glisson basis functions have been presented. In this work, the application of these expressions in the solution of the combined field integral equation (CFIE) is presented. Solutions via analytical expressions of the electric and magnetic fields are verified and compared with the conventional marching-on-in time (MOT) algorithm solutions that employ numerical basis integrations. It is shown that the accuracy and stability of the solutions obtained with the proposed (analytical) approach are better when compared to those obtained with the conventional (numerical) method. In addition, a discussion section about the effect of the proposed approach in solving the electric field integral equation (EFIE) is added. In this section, it is demonstrated that the dependency of the solution via analytical expressions of the fields are less sensitive to the time step size in comparison to the conventional solution, and that the increase in accuracy is a necessary but not sufficient condition for stability.