Homogenisation

Homogenisation replaces a medium with fine-scale structure by an effective medium that reproduces its large-scale behaviour, and makes precise the sense in which the replacement is valid. The effective coefficients are determined by cell problems that the microstructure poses, which is the whole subtlety, since averaging the original coefficients gives the wrong answer. Writing here meets homogenisation through mesh pipelines and representative volume elements, where the microstructure is a geometric object before it is a coefficient.