Physics – Computational Physics
Scientific paper
2002-12-07
Physics
Computational Physics
13 pages, 7 figures
Scientific paper
Recent developments in multiscale computation allow the solution of ``coarse equations'' for the expected macroscopic behavior of microscopically/stochastically evolving particle distributions without ever obtaining these coarse equations in closed form. The closure is obtained ``on demand'' through appropriately initialized bursts of microscopic simulation. The effective coupling of microscopic simulators with macrosocopic behavior embodied in this approach requires certain decisions about the nature of the unavailable ``coarse equation''. Such decisions include (a) the determination of the highest spatial derivative active in the equation, (b) whether the coarse equation satisfies certain conservation laws, and (c) whether the coarse dynamics is Hamiltonian. These decisions affect the number and type of boundary conditions as well as the nature of the algorithms employed in good solution practice. In the absence of an explicit formula for the temporal derivative, we propose, implement and validate a simple scheme for deciding these and other similar questions about the coarse equation using only the microscopic simulator. Microscopic simulations under periodic boundary conditions are carried out for appropriately chosen families of random initial conditions; evaluating the sample variance of certain statistics over the simulation ensemble allows us to infer the highest order of spatial derivatives active in the coarse equation. In the same spirit we show how to determine whether a certain coarse conservation law exists or not, and we discuss plausibility tests for the existence of a coarse Hamiltonian or integrability. We argue that such schemes constitute an important part of the equation-free approach to multiscale computation.
Gear William C.
Kevrekidis Ioannis G.
Kevrekidis Panayotis G.
Li Ju
No associations
LandOfFree
Deciding the Nature of the "Coarse Equation" through Microscopic Simulations: the Baby-Bathwater Scheme does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Deciding the Nature of the "Coarse Equation" through Microscopic Simulations: the Baby-Bathwater Scheme, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deciding the Nature of the "Coarse Equation" through Microscopic Simulations: the Baby-Bathwater Scheme will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-548296