This work initially aimed to explore what Kokkos offers for writing portable code. During the project, we successfully implemented several variants of the P2P inner kernel, achieving interesting performance results. However, while the hierarchical version was expected to outperform the flat versions, this was not exactly the case. Further investigation is therefore needed to develop a more effective hierarchical approach. Moving forward, the goal is now to extend the work done for the basic electrostatic kernel to more generic kernels, allowing us to handle a wider range of interactions, such as:

\begin{equation*} k(x,y) = \frac{(x - y)}{\|x - y\|^3}, \end{equation*} \begin{equation*} k(x,y) = \ln{\bigl\{\| x - y\|\bigl\}}, \end{equation*} \begin{equation*} k(x,y) = \exp{\bigl\{\frac{- \| x - y \|}{ \sigma^2 }\bigl\}}, \end{equation*} \begin{equation*} k(x,y) = 3 \frac{(x - y) \otimes (x - y)}{\|x - y\|^5} - \frac{1}{\|x - y\|} \textbf{I}_{3 \times 3}. \end{equation*}

Such work would actually provide an opportunity to explore the different possibilities offered by Kokkos views. Additionally, it's worth noting that we only tested Kokkos SIMD with a basic kernel that used common operations, and it performed comparably to state-of-the-art libraries like xsimd. It would be worthwhile to repeat these experiments with more complex kernels (involving functions like logarithmic or exponential operations, which lack pre-implemented SIMD intrinsics) to better assess the extent of support compared to other leading SIMD libraries. A future goal, as it was originally planned, would be to integrate Kokkos-based kernels into a program that uses StarPU to explore how these components can be effectively combined.