Finite element technique for solving time-domain Hallen integral equation

The transient response of a thin wire structure is important in numerous applications and also for achieving a more fundamental knowledge of radiation and scattering in general. Most of the known direct time-domain techniques for obtaining the transient response from thin wire structures are based on solving the time domain Pocklington integral equation. The Pocklington integral equation contains the time and the space derivatives within its kernel and their numerical representations are not always satisfactory. Consequently complex numerical procedures have to be used and the method becomes computationally less efficient. On the other hand the Hallen time-domain integral equation does not contain either space or time derivatives, which may seem to be very attractive; but this equation is considered to be difficult for a numerical treatment because of the presence of unknown functions which represent the solutions of the homogeneous wave equation. A new and efficient procedure based on finite element integral equation method (FEIEM) is presented for solving the Hallen equation. The method can be also easily extended to more complex geometries and to half-space problems