Projective and coarse projective integration for problems with continuous symmetries

Kavousanakis, ME; Erban, R; Boudouvis, AG; Gear, CW; Kevrekidis, IG

dc.contributor.author	Kavousanakis, ME	en
dc.contributor.author	Erban, R	en
dc.contributor.author	Boudouvis, AG	en
dc.contributor.author	Gear, CW	en
dc.contributor.author	Kevrekidis, IG	en
dc.date.accessioned	2014-03-01T01:26:56Z
dc.date.available	2014-03-01T01:26:56Z
dc.date.issued	2007	en
dc.identifier.issn	0021-9991	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18290
dc.subject	Coarse projective integration	en
dc.subject	Continuous symmetry	en
dc.subject	Dynamic renormalization	en
dc.subject	Multiscale computation	en
dc.subject	Projective integration	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	NONLINEAR SCHRODINGER-EQUATION	en
dc.subject.other	SELF-SIMILAR SOLUTIONS	en
dc.subject.other	DIFFERENTIAL-EQUATIONS	en
dc.subject.other	STOCHASTIC SIMULATION	en
dc.subject.other	RECONSTRUCTION	en
dc.subject.other	COMPUTATION	en
dc.subject.other	DIFFUSION	en
dc.subject.other	SYSTEMS	en
dc.title	Projective and coarse projective integration for problems with continuous symmetries	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jcp.2006.12.003	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jcp.2006.12.003	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a ""co-evolving"" frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in the new spatial frame. The slower time behavior permits the use of projective and coarse projective integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems, respectively. These methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries. The ideas of projective integration in a co-evolving frame are illustrated on the one-dimensional, translationally invariant Nagumo partial differential equation (PDE). A corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is used to illustrate the coarse-grained method. A simple, one-dimensional diffusion problem is used to illustrate the scale invariant case. The efficiency of projective integration in the co-evolving frame for both the macroscopic diffusion PDE and for a random-walker particle based model is again demonstrated. © 2007 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Computational Physics	en
dc.identifier.doi	10.1016/j.jcp.2006.12.003	en
dc.identifier.isi	ISI:000248854300021	en
dc.identifier.volume	225	en
dc.identifier.issue	1	en
dc.identifier.spage	382	en
dc.identifier.epage	407	en