On the Computation of Power in Volume Integral Equation Formulations
  We present simple and stable formulas for computing power (including absorbed/radiated, scattered and extinction power) in current-based volume integral equation formulations. The proposed formulas are given in terms of vector-matrix-vector products of quantities found solely in the associated linear system. In addition to their efficiency, the derived expressions can guarantee the positivity of the computed power. We also discuss the application of Poynting's theorem for the case of sources immersed in dissipative materials. The formulas are validated against results obtained both with analytical and numerical methods for scattering and radiation benchmark cases. 
A. G. Polimeridis, M. T. H. Reid, S. G. Johnson, J. K. White, A. W.   Rodriguez
physics.comp-ph