Computer simulations allow to study processes that occur in condensed matter on an atomistic level. They give thus a very detailed picture of such processes which frequenty leads to a better understanding of these processes. Simulations methods became in this way an essential part of scientific research. We develop new alogorithms that allow us to do artomistic simulations faster or more accurately. Speed is an important aspect since many scientific simulations require many weeks of computer time even on large supercomputers. Improved accuracy is important for an accurate modelling but it is difficult to achieve since it requires the solution of a many body quantum problem.