LogLatt: A computational library for the calculus and flows on logarithmic lattices

Abstract

Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on multi-dimensional logarithmic lattices. The applicabilities include common differential operators, norms, and convolutions, and operate as MATLAB function handles, so their implementations result in elegant and intuitive scripts. Particularly, when applied to dynamics, users may code the governing equations exactly as they are mathematically written. We give codes and results for some problems of fluid flow as examples of application.