We discuss algorithms for lattice-based computations, in particular lattice reduction, the detection of nearest neighbors, and the computation of clusters of nearest neighbors. We focus on algorithms that are most efficient for low spatial dimensions (typically d = 2, 3) and input data within a reasonably limited range. This makes them most useful for physically oriented numerical simulations, for example of crystalline solids. Different solution strategies are discussed, formulated as algorithms, and numerically evaluated.
Bibliographical noteFunding Information:
This work was supported in part by the Department of Energy under Award Number DE-FG02-05ER25706 and by the University of Minnesota Supercomputing Institute. The authors acknowledge preliminary work performed by Jon Wilkening on the “short-list” method, while working as a postdoctoral fellow on quasicontinuum applications. The authors would like to thank Ryan Elliott for his careful reading of the manuscript and many helpful comments.
- Cluster computation
- Lattice algorithms
- Lattice reduction
- Nearest neighbor