A parallel method for population balance equations based on the method of characteristics. (English) Zbl 1340.65206

Li, Yu; Lin, Qun; Xie, Hehu

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 140-149 (2013).

The paper discusses the parallel numerical discretization of the population balance equations (PBE) that arise in crystallization processes that is of a big importance in industrial applications. The proposed method uses first the method of characteristics to reduce the model size into a series of equations described on the characteristics that are of a small size and more suitable for parallel computation. The model is discretized using Euler in time and finite elements in space. The authors use the shared memory parallelization strategy and the communication between the processors is achieved by each processor using the results of the previous one as initial condition. Convincing numerical tests are shown with a good scalability rate.
For the entire collection see [Zbl 1277.00032].

Reviewer: Lakhdar Remaki (Bilbao)

MSC:

65M22	Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
46N40	Applications of functional analysis in numerical analysis

Keywords:

parallel numerical discretization; characteristics method; population balance equations