Mehrgitterverfahren für die zwei- und dreidimensionale Poissongleichung mit periodischen Randbedingungen und eine Anwendung in der Molekulardynamik

Bioinformatics is playing a significant role in both research and industry. An important part in this area is molecular dynamics which requires powerful soft- and hardware, especially for force field calculations. To solve the occurring three-dimensional Poisson equations with periodic boundary conditions, new geometric multigrid approaches are developed in this diploma thesis. They are as efficient as already known multigrid approaches for the Poisson equation with other boundary conditions. For instance, they reach a complexity (computational work) of O(N) and can be parallelized. Particularly special features and differences to other boundary conditions, regarding the choice of multigrid components, are investigated in this thesis. The developed algorithms are built in a new approach proposed by Takumi Washio for computing force fields. Because of the usage of efficient multigrid approaches its complexity is esentially proportional only to the number of particles in the basic cell in contrast to most of the other known approaches. It yields results with high accuracy and can be applied to systems with millions of particles. Therefore it is a promising alternative to nowadays used FFT- and Multipole approaches especially for the next generation of force field calculation software