Note: if an on-line version and published version are shown, the on-line version is different (usually longer and shortened for publication.)
Manifold defined by points: Parametrizing
and Boundary Detection
Parameterization of non-linear
manifolds, Aug 2012
Analysis and
computation of a discrete KdV-Burgers type equation with fast
dispersion and slow diffusion, with Z. Artstein, I.
G. Kevrekidis, M. Slemrod and E. S. Titi. SINUM 49 #5, pp2124-2143, 2011
Computing
on Virtual Slow Manifolds of Fast Stochastic Systems, with
D. Givon & I. Kevrekids, Mar 2010
Analysis of the accuracy and convergence of equation-free projection to a slow manifold, with A. Zagaris, T. J. Kaper & I. Kevrekidis, Math. Mod. Num. Anal. 43 (4) pp.757-784 (2009)
Invariants of fast solutions of KdV-Burgers
Equations, Sep, 2008
Optimum Choice of Weights in Slope
Calculation with Noisy Data, June, 2008
Backward differentiation formulas. Scholarpedia, 2(8):3162 (2007)
Projective and coarse projective integration
for problems with continuous symmetries, with M. E.
Kavousanakis, R. Erban, A. G. Boudouvis, and I. G. Kevrekidis, to
appear, J. Comp. Phys. (2007)
On-the-Fly Local Error Estimation
for Projective Integrators (with S. L. Lee) LLNL
report UCRL-JRNL-224892 (Oct, 2006)
Towards Explicit Methods for DAEs BIT Num. Math. 46, pp 505-514 (2006)
Second-order
accurate projective integrators for multiscale problems
(with S. L. Lee). JCAM (to
appear) Also Lawrence Livermore Report UCRL-JRNL-212640, June 2005
Constraint-defined manifolds: a
legacy-code approach to low-dimensional computation, (with I. G.
Kevrekidis), J. Sci. Comp. in press, (2004); also
physics/0312094 at arXiv.org.
From Molecular Dynamics to coarse
self-similar solutions: a simple example using equation-free
computation", (with L. Chen, P. G. Debenedetti, & I. G.
Kevrekidis, JNNFM 120 pp.215-223
(2004)
Equation-free: the computer-assisted analysis of complex, multiscale systems, (with I. G. Kevrekidis, & G. Hummer) A.I.Ch.E Journal. 50 (7), pp.1346-1354 (2004)
Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models (with {J. Cisternas, S. Levin & I.G. Kevrekidis} Proc. Roy. Soc. London, in press, (2004); can be found as nlin.AO/0310011 at arXiv.org
Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems, (with R. Rico-Martinez & I. G. Kevrekidis) Journal of Computational Physics, 196, #2, pp 474-489 (2004)
Deciding the Nature of the “Coarse Equation” through Microscopic Simulations (with Ju Li, P. G. Kevrekidis, & I. G. Kevrekidis) SIAM MMS 1(3) pp391-407 (2003)
“The gaptooth method in particle simulations" (with J. Li and I. G. Kevrekidis,), Phys. Lett. A, 316 pp.190-195 (2003).
Telescopic
Projective Methods for Stiff Differential Equations, (with
I. G. Kevrekidis) JCP. 187, #1, pp 95-109,
(2003).
Boundary
processing for Monte Carlo Simulations in the Gap-Tooth Scheme
NECI Technical
Report TR 2002-031N,Oct
2002
Finding
Stationary
States of Noisy Processes, NECI Technical Report TR
2002-025N, Oct 2002
Coarse
Integration/Bifurcation Analysis via Microscopic Simulators:
micro-Galerkin methods, (with I. G. Kevrekidis and
C.Theodoropoulos) NECI Technical Report TR
2001-106, 3 Oct 2001, Comp. Chem. Engng. 26
pp941-963 (2002);
.
Projective
Integration Methods for Distributions, NEC Technical
Report TR 2001-130, 26 Nov, 2001
Projective
Methods for Differential Equations, (with I. G.
Kevrekidis) NECI Technical Report NECI-TR 2001-029, Apr. 2001, also
SIAM J. Sci. Comp. 24(4) pp1091-1106
(2003)
Equation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks, (with I. G. Kevrekidis, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C.Theodoropoulos) Comm. Math. Sciences 1(4) 715-762 (2003); also physics/0209043 at arXiv.org. Original version was NECI Technical Report TR 2002-010N, 19 Aug, 2002