Multiscale modeling of physical phenomena: Adaptive control of models
J. T. Oden, S. Prudhomme, A. Romkes and P. T. Bauman
SIAM Journal on Scientific Computing, 28, 2359-2389 (2006).
ABSTRACT
It is common knowledge that the accuracy with which computer simulations can
depict physical events depends strongly on the choice of the mathematical model
of the events. Perhaps less appreciated is the notion that the error due to
modeling can be defined, estimated, and used adaptively to control modeling
error, provided one accepts the existence of a base model that can serve as a
datum with respect to which other models can be compared. In this work, it is
shown that the idea of comparing models and controlling model error can be used
to develop a general approach for multiscale modeling, a subject of growing
importance in computational science. A posteriori estimates of modeling error in
so-called quantities of interest are derived and a class of adaptive modeling
algorithms is presented. Several applications of the theory and methodology are
presented. These include preliminary work on random multiphase composite
materials, molecular statics simulations with applications to problems in
nanoindentation, and analysis of molecular dynamics models using various
techniques for scale bridging.