Scalable Computation of Long-Range Potentialsfor Molecular Dynamics

Abstract: To calculate long-range potentials in a molecular dynamics simulation, a naive approach using direct particle interactions needs a computational work of order O(N2). This is infeasible for larger simulations. In order to reduce this complexity and thus allow to increase the size of the simulation, several algorithms have been proposed in the last decades. This thesis first gives an overview over these algorithms and examines the advantages and disadvantages of these methods with respect to high performance computing, i.e., how well they are suited for a good scalability on a many-processor system. Two algorithms that seem well suited for this task, the Multilevel Summation Method and the Meshed Continuum Method, both of which are based on a hierarchy of multiple grids, are implemented and optimized for a massively parallel environment. The mathematical foundation as well as the implementation steps to improve the performance and scalability of the algorithms are explained in detail. Finally the algorithms were tested with up to 8192 processors at PDC. The results of these runs are presented together with an explanation of possible performance bottlenecks and a final comparison of both algorithms