HR: 16:20h
AN: A14B-02 INVITED     [Abstracts]
TI: The use of systems and control techniques in equation free modeling of complex multiscale processes
AU: * Kevrekidis, Y G
EM: yannis@princeton.edu
AF: Department of Chemical Engineering, Princeton University, Olden Street, E-quad, Princeton, NJ 0854- United States
AU: * Kevrekidis, Y G
EM: yannis@princeton.edu
AF: Program in Applied and Computational Mathematics, Princeton University, Fine Hall, Princeton, NJ 08540 United States
AB: In current modeling , the best available descriptions of a system often come at a fine level (atomistic, stochastic, microscopic, individual-based) while the questions asked and the tasks required by the modeler (prediction, parametric analysis, optimization and control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by first deriving macroscopic evolution equations from the microscopic models, and then bringing our arsenal of mathematical and algorithmic tools to bear on these macroscopic descriptions. Over the last few years, and with several collaborators, we have developed and validated a mathematically inspired, computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly. We call this the ``equation-free" approach, since it circumvents the step of obtaining accurate macroscopic descriptions. Te backbone of this approach is the design of (computational) experiments. Traditional continuum numerical algorithms can be viewed as a set protocols for experimental design (where "experiment" means a computational experiment set up and performed with a model at a different level of description). Ultimately, what makes it all possible is the ability to initialize computational experiments at will. Short bursts of appropriately initialized computational experimentation -through matrix-free numerical analysis and systems theory tools like feedback, variance reduction and estimation- bridges microscopic simulation with macroscopic modeling.
DE: 3367 Theoretical modeling
DE: 3210 Modeling
SC: Atmospheric Sciences [A]
MN: 2004 AGU Fall Meeting