Tensor train versus Monte Carlo for the multicomponent Smoluchowski coagulation equation

Parallel Numerical Algorithm for Solving Advection Equation for Coagulating Particles

“…As far as coalescence integrals are evaluated sequentially at each processor their calculation can be additionally accelerated by use of GPU and Cuda technology. We will apply our ideas to more intricate multicomponent coagulation models [7,15,23] requiring special implementations of multidimensional convolutions based on utilization of low-rank tensor decompositions [15,21].…”

Sketching for low-rank nonnegative matrix approximation: a numerical study

“…which describes the evolution of the concentration function n(v 1 , v 2 , t) of the two-component particles of size (v 1 , v 2 ) per unit volume. In the previous works [8,9], we showed that the corresponding initial-value problem can be solved by explicit time-integration in low-rank format for a wide range of coagulation kernels K(u 1 , u 2 ; v 1 , v 2 ) and nonnegative initial conditions. This means that at every time instant t the solution n(v 1 , v 2 , t) is represented as a low-rank matrix, which accelerates computation.…”

“…In other applications, however, the main goal is to achieve good compression of the data. This mostly concerns scientific computing in such areas as numerical solution of large-scale differential equations [8][9][10][11][12] and multivariate probability [13,14]. There, NMF can appear to be a bottleneck, since the nonnegative rank might be significantly larger than the usual matrix rank (not to mention the computational complexity of approximate NMF; the exact NMF is NP-hard [15]).…”

Study of industrial titania synthesis using a hybrid particle-number and detailed particle model

“…Popular numerical methods for solving population balance equations include moment-based [26,27,28], sectional [29,30,31] and Monte Carlo [32,33,34,35,36,37] treatments [38]. Although other methods can be optimised to accommodate several particle internal coordinates [39], the stochastic approach is necessary when a detailed particle model is used as this can extend to thousands of internal coordinates (resolving particle connectivity as well as sizes). Direct simulation with a detailed particle model has been used to study titania synthesis in previous work e.g.…”