(2ju) On Improving the Inadequacies in Moment Inversion Algorithm for the Extended Quadrature Method of Moments (EQMOM)

1. Mathematical Modelling for Engineering applications
2. Eigenvalue calculation for large-size non-symmetric matrices

Abstract:

Population balance model (PBM) have wide engineering applications. There is a considerable interest for developing fast, stable and accurate numerical methods to solve population balance equations (PBEs) such as the extended quadrature-based method of moment (EQMOM). However the moment-inversion problem can be ill-conditioned when the number of nodes is increased to improve the accuracy of the solution. To overcome these problems, EQMOM approximates the number density function (NDF) by a convex mixture of kernel density function (KDF) of the same parametric family. In this study, the moment-inversion procedure is modified based on Halley-Ridder (H-R) moment-inversion algorithm. The first aspect focuses on the cases in which the calculation of the root is out of the initial interval, calculation of the multiple root or the lowest root among the roots are very close to each other. For these cases, the roots can only be calculated by the proposed Halley-Ridder (H-R) moment-inversion algorithm. An increase in the number of floating point operations (FLOPS) has been observed which the proposed algorithm responds in limitations mentioned above. The total number of FLOPS for all the kernels, used for the approximation, increased by around 30 %. The identified research gap has been resolved in this study improving the scope of EQMOM which can be considered to be an improvement towards the development of a more reliable and robust moment-inversion procedure.