A novel exact two-point field equation (2PFE) for solving electromagnetic scattering problems

The finite-difference (FD) method is a basic technique for solving differential equations. The disadvantage of it for electromagnetic (EM) problems of an open region is that the mesh needs to be terminated with the application of a proper boundary condition. In this paper, a novel exact two-point field equation (2PFE) is derived from rigorous analysis of the radiation field and it is proposed to be used as the termination boundary condition (BC) for solving EM scattering problems in the open region by the iterative FD method. This 2PFE-BC approaches its exact solution through the iteration process and, at the same time, the scattered field and the induced current density approach their exact solutions. The novel 2PFE is simple in concept and easy to apply. The validity of the 2PFE and the iterative FD method has been tested. Several two-dimensional (2-D) scattering problems have been successfully solved. The results agree very well with those obtained by method of moments (MoM) or measured equation of invariance (MEI).