Equation-Free Multiscale Computation: Enabling Microscopic Simulators to Perform System-Level Tasks

Yannis Kevrekidis
Princeton University

I will discuss a framework for computer-aided multiscale analysis, which enables models at a "fine" (microscopic/stochastic) level of description to perform modeling tasks at a "coarse" (macroscopic, systems) level.

In traditional modeling, macroscopic equations are first derived from microscopic models, and then analyzed with available continuum methods. Our equation-free (EF) approach bypasses the derivation of macroscopic evolution equations, provided these equations conceptually exist but are not available in closed form. The mathematics-assisted development of a computational superstructure enables alternative descriptions of the problem physics (LB, KMC, MD, BD microscopic simulators), executed over relatively short time and space scales, to perform systems level tasks (integration over relatively large time and space scales, "coarse" bifurcation analysis, but also optimization and control tasks) directly.

Return to the Program