On the Monotonic Lagrangian Grid as Antecedent to the Neighborhood Grid

Abstract

We note that a recently described data structure, the Neighborhood Grid, is equivalent to a data structure developed in the mid-1980s called the Monotonic Lagrangian Grid (MLG). The MLG was originally developed to support high-performance molecular and fluid dynamics simulations on both supercomputer and vector processing architectures and still finds use in those and other areas. In this paper we emphasize that the rediscovery of the MLG offers benefits to users of the Neighborhood Grid in the form of an existing literature with results relevant to its efficient implementation in various contexts while users of the MLG similarly benefit from new theoretical results obtained for the Neighborhood grid.