FDTD method can be used to compute the electromagnetic field scattered by the particles. FDTD method only provides
the 6 vector electromagnetic field components ( Ex Ey Ez Hx Hy Hz) in discrete coordinates, and each component
located on different physical point of the so called Yee cell. The values of the components are transient in time domain.
For calculating the specific problem such as absorption cross section, scattering cross section and extinction cross section
of the scatters, we usually integrates the time-averaged Poynting vector across a closed surface surrounding the scatters.
The transient values of the field components derived from FDTD located at the Yee Cell grids must be translated into the
values of the same physical point at the same physical time to get the time-averaged Poynting vectors. By this way we
can get the highly accurate calculation results. The method of integrating the time-averaged Poynting vector over a
certain closed surface is given in the paper. Comparing with the method of integrating the divergence of time-averaged
Poynting vector over the volume region, our method of face integration is not only much more time saving for large size
scatteres, from O(N3) to O(N2) in time complexity, and having a more direct physical meaning, but keeping the same calculating accurateness at the same time. We calculate the scattering efficiencies and the absorption efficiencies of the sphere of gold in 825 nm incident wave length, in size parameter ranging from 0.5 to 10 and from 0.1 to 1, respectively. The results of our calculation are compared with Mie theory, which are analytical results, to verify the correctness and the accurateness of our method. The spring models for simulating nano coil structures are studied by our method.