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Daniel Tameling

AICES Doctoral Fellow/Improved algorithms for long-range methods in molecular simulations

Dipl.-Ing. in Maschinenbau, Karlsruhe Institute of Technology (2011)

Co-supervised by Paolo Bientinesi (AICES)

Location: Schinkelstrasse 2, Room 431b
Phone: +49 (0)241 80-99140

Pair potentials are ubiquitous in molecular simulations. If, due to the accuracy required for a particular application, use of a cutoff is not an option, the resulting direct algorithm will have a quadratic complexity, since the interaction of each particle with every other particle has to be computed. Thus, the efficient calculation of such long-range pair-potentials is a challenging task. Today, the most widely-used methods are based on an approach first introduced by Ewald in 1921. This approach splits the pair potential into a short-ranged and a long-ranged part. For the former, a cutoff can be applied without losing accuracy while the second is evaluated in Fourier space. This alone yields faster convergence of the potential, but does not improve the complexity. Nevertheless, if Fast Fourier Transforms (FFTs) are used, as is done in mesh-based Ewald methods, the complexity of the whole algorithm is reduced to O(N log N).

However, for large simulations it seems that not only are FFTs the limiting factor in the efficiency of the simulation, but their use is also not optimal. For this reason some new methods that avoid FFTs have been introduced in recent years. These methods have to be investigated more deeply and are therefore the subject of active research. Furthermore, it is necessary to extend these methods to other kinds of potentials than the Coulomb potential, where still most of the research is done. Since the application of these new methods to other potentials is just getting into the focus of interest, there is a variety of topics that need to be covered.
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Decomposition of dispersion forces into short- and long-range components