89 citations · 93 across the 7 of their papers we have counts for
6 papers · 1 filter
Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes
C. W. Gear, T. J. Kaper, I. G. Kevrekidis +1
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using…
From molecular dynamics to coarse self-similar solutions: A simple example using equation-free computation
L. Chen, P. G. Debenedetti, C. W. Gear +1
In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solut…
Constraint-defined Manifolds: a Legacy Code Approach to Low-dimensional Computation
C. W. Gear, I. G. Kevrekidis
If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform co…
Deciding the Nature of the "Coarse Equation" through Microscopic Simulations: the Baby-Bathwater Scheme
Ju Li, Panayotis G. Kevrekidis, C. William Gear +1
Recent developments in multiscale computation allow the solution of ``coarse equations'' for the expected macroscopic behavior of microscopically/stochastically evolving particle d…
Boundary processing for Monte Carlo Simulations in the Gap-Tooth Scheme
C. W. Gear, Ioannis G. Kevrekidis
This note reports on a scheme for interpolating the boundary conditions be- tween non-adjacent modeling regions when the model is based on Monte-Carlo computations of a collection…
Equation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks
Ioannis G. Kevrekidis, C. William Gear, James M. Hyman +3
We present and discuss a framework for computer-aided multiscale analysis, which enables models at a "fine" (microscopic/stochastic) level of description to perform modeling tasks…