Coarse projective kMC integration: forward/reverse initial and boundary value problems
Abstract
In "equationfree" multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarsegrained, macroscopic dynamics can be described by closed equations involving only coarse variables. These variables are typically various loworder moments of the distributions evolved through the microscopic model. We consider the problem of integrating these unavailable equations by acting directly on kinetic Monte Carlo microscopic simulators, thus circumventing their derivation in closed form. In particular, we use projective multistep integration to solve the coarse initial value problem forward in time as well as backward in time (under certain conditions). Macroscopic trajectories are thus traced back to unstable, sourcetype, and even sometimes saddlelike stationary points, even though the microscopic simulator only evolves forward in time. We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of "coarse limit cycles" of the macroscopic behavior, and the approximation of their stability through estimates of the leading "coarse Floquet multipliers".
 Publication:

Journal of Computational Physics
 Pub Date:
 May 2004
 DOI:
 10.1016/j.jcp.2003.11.005
 arXiv:
 arXiv:nlin/0307016
 Bibcode:
 2004JCoPh.196..474R
 Keywords:

 Nonlinear Sciences  Cellular Automata and Lattice Gases
 EPrint:
 Submitted to Journal of Computational Physics