The Fast Multipole Method - Alternative Gradient Algorithm and Parallelization

This thesis describes the Fast Multipole Method (FMM). The method reduces the complexity of the Coulomb problem from O(N$^{2}$) to O(N) and is therefore called a fast Coulomb solver. The FMM is advantageous for the calculation of pairwise interactions, especially for large systems. This work is divided in three parts. The first part addresses the fundamentals of the FMM. The second part discusses the force calculation with the gradient. Two different implementations of the gradient are discussed. The last part shows the parallelization of the FMM. The procedure is described exemplarily for one pass