A Parallel Method for Population Balance Equations Based on the Method   of Characteristics
  In this paper, we present a parallel scheme to solve the population balance equations based on the method of characteristics and the finite element discretization. The application of the method of characteristics transform the higher dimensional population balance equation into a series of lower dimensional convection-diffusion-reaction equations which can be solved in a parallel way.Some numerical results are presented to show the accuracy and efficiency. 
Yu Li, Qun Lin, Hehu Xie
math.NA