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

TL;DR

LogLatt is a MATLAB library that facilitates calculus on multi-dimensional logarithmic lattices, enabling efficient modeling of multi-scale nonlinear physics with intuitive scripting and exact equation coding.

Contribution

It introduces LogLatt, a novel MATLAB library for calculus on logarithmic lattices, enhancing modeling capabilities in multi-scale nonlinear physics.

Findings

Efficient implementation of differential operators, norms, and convolutions.

Application examples in fluid flow demonstrate the library's utility.

Codes provided show accurate modeling of complex dynamics.

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.