Efficiency of particle search methods in smoothed particle hydrodynamics: a comparative study (part I)

Nearest neighbour searching is central to the efficiency of smoothed particle hydrodynamics (SPH). Here the performance of the brute force (BF) or direct search (DS), the cell-linked list (CLL), and the KD-tree (KDT) methods in vectorised form are analysed. The results indicate that the efficiency of the SPH calculations is improved with the vectorised cell-linked list (VCLL) and the vectorised KD-tree (VKDT). However, the VKDT approach is more efficient than the VCLL method for N ≤ 10⁵ in two dimensions (2D) and N ≤ 10⁶ in three dimensions (3D). For larger N, the time duration of the SPH calculations with the VKDT method grows steeply while a linear trend is maintained with the VCLL. The complexity here is measured not only for early events but also close to the point of hardware limit, in which the complexity has a different behaviour, which can be measured and compared using a power fit.