On energy conservation and the method of moments in scattering problems

Electromagnetic scattering problems, including waveguide discontinuity, phased array, and scattering (exterior type) problems, are frequently described by integral equations that can be solved by the Ritz-Galerkin or generalized method of moments. Under appropriate conditions, it has been shown that reciprocity and variational properties are, in fact, preserved in the approximate solutions. It is shown here that in the Ritz-Galerkin method, energy is also conserved under certain conditions, even in those scattering problems where reciprocity does not exist. Hence energy conservation cannot serve as a check for accuracy of a numerical solution obtained by the Ritz method or other related methods.