89 citations · 186 across the 17 of their papers we have counts for
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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…
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…
The gap-tooth scheme for homogenization problems
Giovanni Samaey, Dirk Roose, Ioannis G. Kevrekidis
An important class of problems exhibits smooth behaviour in space and time on a macroscopic scale, while only a microscopic evolution law is known. For such time-dependent multi-sc…
Damping factors for the gap-tooth scheme
Giovanni Samaey, Ioannis G. Kevrekidis, Dirk Roose
An important class of problems exhibits macroscopically smooth behaviour in space and time, while only a microscopic evolution law is known. For such time-dependent multi-scale pro…
Effective equations for discrete systems: A time stepper based approach
J. Moeller, O. Runborg, P. G. Kevrekidis +2
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse mo…
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…