Einladung zum Vortrag im Kolloquium Systemdynamik und Prozesstechnik

Equation-Free Multiscale Computation:
Enabling Microscopic Timesteppers to perform System-Level Tasks

Prof. Yannis G. Kevrekidis, Ph.D. , Princeton University

    Zeit: Montag · 15. 7. 2002 · 15:00 Uhr
    Ort: Hörsaal V 9. 12 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

Textbook models of reaction and transport processes typically come in the form of conservation equations (mass, species, momentum, energy) closed through constitutive equations (e.g. the representation of viscous stresses for Newtonian fluids, or mass-action chemical kinetics expressions). In contemporary engineering modeling we have entered an era --- ushered through materials modeling as well as systems biology modeling --- where the time-honored macroscopic conservation equations are often not available any more. Instead, microscopic evolution rules, such as Molecular Dynamics, Monte Carlo or Kinetic Schemes are available, at various levels of coarse-graining.
In this talk we will explore computational approaches combining microscopic simulators with computational superstructures inspired from continuum numerical analysis, system identification, large scale iterative linear algebra and applied bifurcation theory. These approaches (based on the so-called "coarse time-stepper") promise to bypass the derivation of explicit macroscopic equations, while still being able to deliver systems level information operating directly on the microscopic evolution rules. An anthology of examples will be presented, including kinetic models of multiphase flows and reaction-diffusion systems, Monte-Carlo studies of surface reactions, as well as effective medium calculations for reaction and transport in complex media. We will discuss how the "coarse time-stepper" can provide a bridge between microscopic simulation and traditional computational control/optimization methodologies. Additional developments of the basic methodology (such as the computation of self-similar and "coarsely self-similar" solutions) will also be addressed. This work involves a number of collaborators that will be mentioned during the talk.