A New time Integration Scheme for Cahn-hilliard Equations

Handle URI:
http://hdl.handle.net/10754/556646
Title:
A New time Integration Scheme for Cahn-hilliard Equations
Authors:
Schaefer, R.; Smol-ka, M.; Dalcin, L; Paszyn'ski, M.
Abstract:
In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
A New time Integration Scheme for Cahn-hilliard Equations 2015, 51:1003 Procedia Computer Science
Publisher:
Elsevier BV
Journal:
Procedia Computer Science
Conference/Event name:
International Conference on Computational Science, ICCS 2002
Issue Date:
1-Jun-2015
DOI:
10.1016/j.procs.2015.05.244
Type:
Conference Paper
ISSN:
18770509
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S1877050915010522
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSchaefer, R.en
dc.contributor.authorSmol-ka, M.en
dc.contributor.authorDalcin, Len
dc.contributor.authorPaszyn'ski, M.en
dc.date.accessioned2015-06-10T11:30:48Zen
dc.date.available2015-06-10T11:30:48Zen
dc.date.issued2015-06-01en
dc.identifier.citationA New time Integration Scheme for Cahn-hilliard Equations 2015, 51:1003 Procedia Computer Scienceen
dc.identifier.issn18770509en
dc.identifier.doi10.1016/j.procs.2015.05.244en
dc.identifier.urihttp://hdl.handle.net/10754/556646en
dc.description.abstractIn this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.en
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877050915010522en
dc.rightsArchived with thanks to Procedia Computer Science, Under a Creative Commons license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectnon-stationary problemsen
dc.subjectGMRES solveren
dc.subjectCahn-Hilliard equationsen
dc.subjectisogeometric analysisen
dc.titleA New time Integration Scheme for Cahn-hilliard Equationsen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2002-04-21 to 2002-04-24en
dc.conference.nameInternational Conference on Computational Science, ICCS 2002en
dc.conference.locationAmsterdam, NLDen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionAGH University of Science and Technology, Krakow, Polanden
kaust.authorDalcin, Lisandroen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.