Among all the steps involved in DD simulations, the computation of the internal elastic forces and energy are by far the most resources consuming. However, since these are long-ranged and fast decreasing interactions, hierarchical algorithms like the Fast Multipole Method (FMM) are well suited for their fast evaluation. The relatively low accuracy required for the interaction forces between dislocations brought us to develop a more efficient approximation method for the farfield. On the other hand, the nearfield interactions are still evaluated analytically, which required a rather performant implementation (AVX, GPU...). Regarding parallelism, our code benefits from a hybrid OpenMP/MPI paradigm and a cache-conscious data structure. Finally, an accurate handling of topological elements intersecting the structure of the octree was considered. The latter feature implied careful modifications of the P2M/L2P operators in order to deal with shared memory model of parallelism.