Scalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Scheme

Handle URI:
http://hdl.handle.net/10754/624044
Title:
Scalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Scheme
Authors:
Woźniak, M.; Smołka, M.; Cortes, Adriano Mauricio ( 0000-0002-0141-9706 ) ; Paszyński, M.; Schaefer, R.
Abstract:
We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.
KAUST Department:
King Abdullah University of Science and Technology, Thuwal, , Saudi Arabia
Citation:
Woźniak M, Smołka M, Cortes A, Paszyński M, Schaefer R (2016) Scalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Scheme. Procedia Computer Science 80: 834–844. Available: http://dx.doi.org/10.1016/j.procs.2016.05.373.
Publisher:
Elsevier BV
Journal:
Procedia Computer Science
Conference/Event name:
International Conference on Computational Science, ICCS 2016
Issue Date:
2-Jun-2016
DOI:
10.1016/j.procs.2016.05.373
Type:
Article
ISSN:
1877-0509
Sponsors:
The work of MW, MS, MP, RS presented in this paper concerning the development of Cahn-Hilliard scheme has been supported by National Science Centre, Poland grant no. DEC-2012/07/B/ST6/01229. The visit of AC and his work concerning the PETIGA solver interface has been supported by National Science Centre, Poland grant no. DEC-2012/06/M/ST1/00363.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S1877050916308481
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorWoźniak, M.en
dc.contributor.authorSmołka, M.en
dc.contributor.authorCortes, Adriano Mauricioen
dc.contributor.authorPaszyński, M.en
dc.contributor.authorSchaefer, R.en
dc.date.accessioned2017-06-05T06:02:24Z-
dc.date.available2017-06-05T06:02:24Z-
dc.date.issued2016-06-02en
dc.identifier.citationWoźniak M, Smołka M, Cortes A, Paszyński M, Schaefer R (2016) Scalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Scheme. Procedia Computer Science 80: 834–844. Available: http://dx.doi.org/10.1016/j.procs.2016.05.373.en
dc.identifier.issn1877-0509en
dc.identifier.doi10.1016/j.procs.2016.05.373en
dc.identifier.urihttp://hdl.handle.net/10754/624044-
dc.description.abstractWe study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.en
dc.description.sponsorshipThe work of MW, MS, MP, RS presented in this paper concerning the development of Cahn-Hilliard scheme has been supported by National Science Centre, Poland grant no. DEC-2012/07/B/ST6/01229. The visit of AC and his work concerning the PETIGA solver interface has been supported by National Science Centre, Poland grant no. DEC-2012/06/M/ST1/00363.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S1877050916308481en
dc.rightsUnder a Creative Commons license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectCahn-Hilliard equationsen
dc.subjectIsogeometric analysisen
dc.subjectMulti-frontal parallel direct solveren
dc.subjectNon-stationary problemsen
dc.subjectParallel efficiency and speedupen
dc.titleScalability of Direct Solver for Non-stationary Cahn-Hilliard Simulations with Linearized time Integration Schemeen
dc.typeArticleen
dc.contributor.departmentKing Abdullah University of Science and Technology, Thuwal, , Saudi Arabiaen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2016-06-06 to 2016-06-08en
dc.conference.nameInternational Conference on Computational Science, ICCS 2016en
dc.conference.locationSan Diego, CA, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionAGH University of Science and Technology, Krakow, , Polanden
kaust.authorCortes, Adriano Mauricioen
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