Fast Algorithm for the Continuous Solution of the Population Balance Equation

Population balance models are used because of different system heterogeneities due to complex prevailing phenomena governed by particle fusion, splitting and growth. We present a Minimum Relative Entropy Population Density Estimator (MREPDE) based on the fast Clenshaw algorithm for the evaluation of the Legendre series as the heart of our proposed scheme. The present MREPDE reduced the order of computational complexity from O(M2) to O(M) with an accelerated implementation due to the low rank of the particle fusion matrix because of its tensorial decomposition. We implement the PBE and the MREPDE in a fully vectorized form, which results in a linear scaling of the CPU time with respect to M, instead of a cubic scaling using conventional methods. Therefore, our method is suitable for solving large-scale problems involving particle size distributions.