Thursday, February 3, 2005 at 11h (Celestijnenlaan 200A, room S.00.03)
Patch dynamics for multiscale problems
by Giovanni Samaey (Scientific Computing Research Group, KULeuven)
An important class of problems exhibits smooth behaviour on macroscopic space and time scales, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, an ``equation-free" framework has been proposed, of which patch dynamics is an essential component. Patch dynamics is designed to perform numerical simulations of an unavailable macroscopic equation on macroscopic time and length scales; it uses appropriately initialized simulations of the available microscopic model in a number of small boxes (patches), which cover only a fraction of the space-time domain. To reduce the effect of the artificially introduced box boundaries, we use buffer regions to ``shield" the boundary artefacts from the interior of the domain for short time intervals.
We give an overview of the work that lead to the development of this scheme, analyze the accuracy for a model diffusion homogenization problem with periodic heterogeneity, and propose a simple heuristic to determine a sufficient buffer size. The algorithm performance is illustrated through a set of numerical examples, which include a non-linear reaction-diffusion equation and the fourth order Kuramoto--Sivashinsky equation.
Giovanni Samaey is research assistant of the FWO-Vlaanderen