Reciprocity, discretization, and the numerical solution of direct and inverse electromagnetic radiation and scattering problems

The author gives a formulation, based on Lorentz reciprocity, that unifies the finite element method (FEM) and the integral equation models. Wave propagation and scattering problems in electromagnetics have to be addressed with the aid of numerical techniques. Many of these methods can be envisaged as being discretized versions of appropriate weak formulations of the pertinent operator (differential or integral) equations. For the relevant problems as formulated in the time Laplace-transform domain it is shown that the Lorentz reciprocity theorem encompasses all known weak formulations, while its discretization leads to the discretized forms of the corresponding operator equations, in particular to their finite-element and integral-equation modeling schemes. Both direct (forward) and inverse problems are discussed