The n-body problem has various applications in different fields of science such as astrophysics, where it describes the problem of calculating the movements of n different bodies which all interact with each other over time. There exist different algorithms that solve the n-body problem, for example, the naive approach and the Barnes-Hut algorithm. Since applications of the n-body problem can deal with large systems of bodies it is crucial to understand the runtime behavior of theses algorithms.

In this thesis the runtime behavior of the naive algorithm and the Barnes-Hut algorithm will be compared on different CPUs as well as on GPUs from different vendors. Both algorithms will be implemented using SYCL which is an abstraction layer that enables parallel programming for various types of devices. With SYCL there is no need to use different languages for parallel programming on CPUs and GPUs and the whole code can be written using standard C++.

The results show that one can achieve better performance with both algorithms on GPUs than on CPUs. A projection for the runtime of a simulation of approximately one earth year with a system of over 1.2 million bodies and a $\Delta t$ of one hour shows that an NVIDIA A100 GPU could finish this simulation in under one day with the naive approach. A dual socket AMD EPYC 7543 would take almost twelve days for the same simulation. This shows that the naive algorithm maps extremely well to GPUs. CPUs can keep up better with the Barnes-Hut algorithm. Here the projection of the runtime showed that the NVIDIA A100 would finish the simulation of an earth year in just below an hour whereas the dual socket AMD EPYC 7543 could finish the simulation in 2.59 hours.