Design, implementation, and error analysis of the multilevel summation method for dispersion

  • Entwicklung, Implementierung und Fehleranalyse der Multilevel Summation Methode für Dispersion

Tameling, Daniel; Ismail, Ahmed E. (Thesis advisor); Bientinesi, Paolo (Thesis advisor); Mitsos, Alexander (Thesis advisor)

Aachen (2017, 2018)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2017


In molecular simulations, dispersion interactions are the only type of attractive interaction that occurs between all pairs of atoms, and as such they play an important role for a wide range of physical effects. Despite being short-ranged in nature, dispersion interactions can in certain situations be calculated faster if a long-range method is used. The currently most popular long-range solvers are the mesh-based Ewald methods. However, it is well-known that these methods do not scale well to large core counts, whereas growing simulations sizes and the increasing parallelism in computer architectures demand highly scalable algorithms. An alternative long-range method is the multilevel summation, which has been shown to scale extremely well. The main objective of this dissertation is to adapt the multilevel summation to the calculation of dispersion interactions. In particular, an implementation of this method is presented that is not only significantly faster than its electrostatic counterpart from the simulation software LAMMPS but also maintains the good scalability. Moreover, the deficiencies of the existing error estimates for the multilevel summation are discussed, and an improved error estimate is derived. Finally, various means to increase the accuracy of the multilevel summation are presented, among others a correction factor and an adaptive version of the method.