Parallelization of the Softened Gauss Algorithm

Abstract

The computational cost of standard N-body simulation methods is high, making it difficult to study the long-term evolution of secular systems. The Softened Gauss algorithm provides a more efficient alternative by averaging each particle’s motion along its orbit, forming rings. However, it still requires costly quadrature evalua- tions. Building on the CPU-based Softened Gauss implementation of Touma et al. (originally written in C and later parallelized for shared and distributed-memory CPUs), this thesis develops a GPU-parallel implementation of the force and energy evaluations and restructures the underlying quadrature algorithms to expose fine- grained parallelism well suited to the GPU execution model. Experiments demon- strate that an optimized GPU implementation on an NVIDIA B200 GPU achieves more than 15x speedup over an AMD EPYC 9654 96-core CPU baseline. This im- proved performance drastically reduces the cost of computation, while maintaining the numerical accuracy. The proposed implementation enables the simulation of much larger systems with more than 10,000 particles and to follow their evolution for billions of years, thus approaching more realistic astrophysical scenarios.