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|Title:||Patch dynamics for macroscale modelling in one dimension|
|Citation:||ANZIAM Journal, 2012 / vol.53, iss.SUPPL, pp.280-295|
|Publisher:||Cambridge University Press|
|Conference Name:||Engineering Mathematics and Applications Conference (04 Dec 2011 - 07 Dec 2011 : Australia)|
|Department:||Faculty of Engineering, Computer & Mathematical Sciences|
|Abstract:||We discuss efficient macroscale modelling of microscale systems using patch dynamics. This pilot study effectively homogenises microscale varying diffusion in one dimension. The `equation free' approach requires that the microscale model be solved only on small spatial patches. Suitable boundary conditions ensure that these patches are well coupled. By centre manifold theory, an emergent closed model exists on the macroscale. Patch dynamics systematically approximates this macroscale model. The modelling is readily adaptable to higher dimensions and to reaction-diffusion equations.|
|Keywords:||multiscale modelling; patch dynamics; coupled boundary conditions; difference equations|
|Description:||Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference (EMAC2011) held at University Technology Sydney in December 2011|
|Rights:||© Austral. Mathematical Soc. 2012.|
|Appears in Collections:||Applied Mathematics publications|
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