Time domain vector potential formulation for the solution of electromagnetic problems

Several techniques have been proposed for the solution of Maxwell's equations, such as FDTD, which rely on discretization of Maxwell's equations in time. These techniques are attractive because of their simplicity but are limited to dealing with structures with low dispersion characteristics. Other techniques such as condensed TLM offer superior characteristics in terms of dispersion but are more demanding in terms of computer resources. Attempts to use the vector potential formulation by discretization of the vector potential wave equation have also been made in the past. Although the scheme is attractive because of some of the advantages of the TLM technique, they have the shortcoming of the difficulties in implementing metal boundaries. In this paper a new technique for the solution of scattering problems based on discretization of Maxwell's equations in vector potential form (VP) is presented. This new technique maintains the advantage of condensed node representation as in the vector potential formulation, but offers an easy way to treat metal boundaries.