89 citations · 275 across the 19 of their papers we have counts for
4 papers · 1 filter
Patch dynamics with buffers for homogenization problems
Giovanni Samaey, Ioannis G. Kevrekidis, Dirk Roose
An important class of problems exhibits smooth behaviour on macroscopic space and time scales, while only a microscopic evolution law is known. For such time-dependent multi-scale…
An Equation-Free Approach to Nonlinear Control: Coarse Feedback Linearization With Pole-Placement
C. I. Siettos, I. G. Kevrekidis, N. Kazantzis
We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Fee…
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…
Newton-Krylov solvers for time-steppers
C. T. Kelley, I. G. Kevrekidis, L. Qiao
We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations.For a class of dissipative problems, wh…