Physical Sciences and Mathematics Commons^™

Deciding The Nature Of The Coarse Equation Through Microscopic Simulations: The Baby-Bathwater Scheme, J Li, Pg Kevrekidis, Cw Gear, Pg Kevrekidis

Panos Kevrekidis

Recent developments in multiscale computation allow the solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations in closed form. The closure is obtained on demand through appropriately initialized bursts ofmicroscopic simulation. The effective coupling of microscopic simulators with macrosocopic behavior requires certain decisions about the nature of the unavailable coarse equation. Such decisions include (a) the highest spatial derivative active in the coarse equation, (b) whether the equation satisfies certain conservation laws, and (c) whether the coarse dynamics is Hamiltonian. These decisions affect the number and type of boundary conditions …