Multiscale modelling of microscale heterogeneous systems: analysis supports systematic and efficient macroscale modelling and simulation

TL;DR

This paper discusses new mathematical and computational approaches for multiscale modelling of heterogeneous materials, providing a toolbox for efficient macroscale simulations based on microscale analysis.

Contribution

It introduces novel multiscale modelling techniques and computational tools specifically designed for heterogeneous media, enhancing systematic and efficient macroscale simulation capabilities.

Findings

Development of a multiscale modelling toolbox

Implementation of equation-free computational methods

Enhanced efficiency in macroscale simulations

Abstract

These are lecture notes for five sessions in the AMSI Winter School on 'Computational Modelling of Heterogeneous Media' held at QUT in July 2019 [https://ws.amsi.org.au/]. Aim: Discuss a mix of new mathematical approaches for multiscale modelling, heterogeneous material in particular, along with corresponding novel computational techniques and issues. I include discussion of a developing toolbox that empowers you to implement effective multiscale `equation-free' computation [https://github.com/uoa1184615/EquationFreeGit.git].