FFT-based evaluation of multivariate aggregation integrals in population balance equations on uniform tensor grids

We consider the numerical solution of the multivariate aggregation population balance equation on a uniform tensor grid. We introduce a multidimensional fast Fourier transformation for the efficient evaluation of the aggregation integrals leading to a reduction in the complexity order of the algorithm compared to the direct evaluation approach. We illustrate the new evaluation algorithm for two discretizations, an FEM approach as well as the sectional method. We discuss the conservation of moments for these methods and provide numerical comparisons illustrating the superior performance of FFT-based algorithms. We also discuss and numerically illustrate their potential for parallelization.