Patch dynamics for macroscale modelling in one dimension


  • Judith Bunder University of Adelaide
  • A. J. Roberts University of Adelaide



multiscale modelling, patch dynamics, coupled boundary conditions, difference equations


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. References
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Author Biographies

Judith Bunder, University of Adelaide

School of Mathematical Science, PostDoc

A. J. Roberts, University of Adelaide

Professor of Applied Maths





Proceedings Engineering Mathematics and Applications Conference