Once the density distribution is found, the potential energy of each point in the mesh can be determined from the differential form of Gauss's law, which—after identifying the electric field E as the negative gradient of the electric potential Φ —gives rise to a Poisson equation that is easily solved after applying the Fourier transform. Thus it is faster to do a PM calculation than to simply add up all the interactions on a particle due to all other particles for two reasons: firstly, there are usually fewer grid points than particles, so the number of interactions to calculate is smaller, and secondly the grid technique permits the use of Fourier transform techniques to evaluate the potential, and these can be very fast.