The Dual Quadrature Method of Generalized Moments (DuQMoGeM) is an accurate moment method for solving the population balance equation (PBE). The drawback of DuQMoGeM is the high computational cost associated with numerical integrations of the PBE integral terms in which each integrand can be integrated independently and, therefore, amenable to parallelization on GPUs. In this work, two parallel adaptive cubature algorithms were implemented on a hybrid architecture (CPU-GPU) to accelerate the DuQMoGeM. The speedup and scalability of these parallel algorithms were studied with different types of Genz's test functions. Then, we applied these parallel numerical integration algorithms in the DuQMoGeM solution of the PBE for three bivariate cases, obtaining speedups between 11 and 15. (C) 2013 Elsevier Ltd. All rights reserved.