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Finding the exact close neighbors of each fluid element in mesh-freecomputational hydrodynamical methods, such as the Smoothed ParticleHydrodynamics (SPH), often becomes a main bottleneck for scaling theirperformance beyond a few million fluid elements per computing node. Treestructures are particularly suitable for SPH simulation codes, which rely onfinding the exact close neighbors of each fluid element (or SPH particle). Inthis work we present a novel tree structure, named \textit{$b$-tree}, whichfeatures an adaptive branching factor to reduce the depth of the neighborsearch. Depending on the particle spatial distribution, finding neighbors using\tree has an asymptotic best case complexity of $O(n)$, as opposed to $O(n \logn)$ for other classical tree structures such as octrees and quadtrees. We alsopresent the proposed tree structure as well as the algorithms to build it andto find the exact close neighbors of all particles. We assess the scalabilityof the proposed tree-based algorithms through an extensive set of performanceexperiments in a shared-memory system. Results show that b-tree is up to$12\times$ faster for building the tree and up to $1.6\times$ faster forfinding the exact neighbors of all particles when compared to its octree form.Moreover, we apply b-tree to a SPH code and show its usefulness over theexisting octree implementation, where b-tree is up to $5\times$ faster forfinding the exact close neighbors compared to the legacy code.

Finding Neighbors in a Forest: A b-tree for Smoothed Particle Hydrodynamics Simulations