Performance Characteristics of TreePM codes
  We present a detailed analysis of the error budget for the TreePM method for doing cosmological N-Body simulations. It is shown that the choice of filter for splitting the inverse square force into short and long range components suggested in Bagla (2002) is close to optimum. We show that the error in the long range component of the force contributes very little to the total error in force. Errors introduced by the tree approximation for the short range force are different from those for the inverse square force, and these errors dominate the total error in force. We calculate the distribution function for error in force for clustered and unclustered particle distributions. This gives an idea of the error in realistic situations for different choices of parameters of the TreePM algorithm. We test the code by simulating a few power law models and checking for scale invariance. 
J.S. Bagla and Suryadeep Ray