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dc.contributor.authorSchaefer, R.
dc.contributor.authorSmol-ka, M.
dc.contributor.authorDalcin, Lisandro
dc.contributor.authorPaszyn'ski, M.
dc.date.accessioned2015-06-10T11:30:48Z
dc.date.available2015-06-10T11:30:48Z
dc.date.issued2015-06-01
dc.identifier.citationA New time Integration Scheme for Cahn-hilliard Equations 2015, 51:1003 Procedia Computer Science
dc.identifier.issn18770509
dc.identifier.doi10.1016/j.procs.2015.05.244
dc.identifier.urihttp://hdl.handle.net/10754/556646
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.
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877050915010522
dc.rightsArchived with thanks to Procedia Computer Science, Under a Creative Commons license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectnon-stationary problems
dc.subjectGMRES solver
dc.subjectCahn-Hilliard equations
dc.subjectisogeometric analysis
dc.titleA New time Integration Scheme for Cahn-hilliard Equations
dc.typeConference Paper
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalProcedia Computer Science
dc.conference.date2002-04-21 to 2002-04-24
dc.conference.nameInternational Conference on Computational Science, ICCS 2002
dc.conference.locationAmsterdam, NLD
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionAGH University of Science and Technology, Krakow, Poland
kaust.personDalcin, Lisandro
refterms.dateFOA2018-06-13T12:21:57Z
dc.date.published-online2015-06-01
dc.date.published-print2015


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