Neglex

Neglex refers to a family of algorithms used in computational physics, particularly in the context of the boundary element method (BEM). These algorithms are designed to accelerate the computation of sums of interactions between discrete elements, such as charges or particles. The core idea behind neglex is to group elements that are far apart and then approximate their collective interaction using a multipole expansion, rather than calculating the interaction between every pair of elements individually. This significantly reduces the computational complexity from O(N^2) to roughly O(N log N) or O(N), where N is the number of elements.

The name "neglex" is a portmanteau derived from "near-field" and "far-field," reflecting the algorithm's strategy of treating interactions differently based on the distance between elements. Close-by elements are treated directly, while distant groups of elements are handled through approximations. This hierarchical approach allows for efficient calculation of forces and potentials in systems with many interacting components, such as molecular dynamics simulations, electrostatic problems, and fluid dynamics. Variants of neglex, like the Fast Multipole Method (FMM), share similar principles and are widely adopted for their efficiency in handling large-scale problems. The development and application of neglex algorithms have been crucial for advancing simulations in various scientific and engineering disciplines.