Power conservation in method of moments and finite-element method for radiation problems

Conservation of energy and power can be, under certain conditions, exactly satisfied in an approximate numerical method. In this paper necessary and sufficient conditions for this property are rigorously derived for the finite-element method (FEM) and the method of moments (MoM). Two boundary formulations of FEM (strong and weak) and three formulations of MoM (MoM/VIE, MoM/SIE for metallic and MoM/SIE for dielectric bodies) were considered for radiation problems in the frequency domain. The concept of error generators-fictitious generators that produce the difference between the approximate and the exact solution-was introduced to state the power conservation property from another aspect. It was proved that, for the appropriate governing equation and the "conjugated" inner product, power conservation is satisfied if and only if the Galerkin (or equivalent) method is used. However, power conservation is corrupted if an equivalence principle (surface or volume) is utilized in MoM to solve problems in inhomogeneous media. Examples are given to illustrate the power conservation and its possible advantages.