Germany; Russia Jena; Moscow; Pereslavl-Zalessky; Yekaterinburg
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Section
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Computer science
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Title
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The effectiveness of parallelizing an algorithm of the PFC equation solution using PetIGA library
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Author(-s)
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Starodumov I.O.a,
Pavlyuk E.V.a,
Abramov S.M.b,
Klyuev L.V.c,
Galenko P.K.d,
Alexandrov D.V.a
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Affiliations
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Ural Federal Universitya,
Program Systems Institute, Russian Academy of Sciencesb,
Immers Ltdc,
University of Jenad
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Abstract
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The paper presents an algorithm for solving the equation of Phase Field Crystal (PFC) in a hyperbolic statement that allows to describe the phase transitions of metastable or unstable state at the nuclear density scale, described by a differential equation of the sixth order with respect to the space variable and the second order with respect to the time variable. The algorithm is based on the method of isogeometric analysis (IGA) and is implemented by PetIGA library. The resulting code allows parallel computations, which significantly speeds up the process of solving a problem. The effectiveness of used instruments during the calculations on high-performance computing clusters is evaluated. An analysis of the effectiveness of the current algorithm is carried out for heterogeneous computer systems.
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Keywords
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phase field crystal, high performance computation, isogeometric analysis
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UDC
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519.711.3
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MSC
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65D05
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DOI
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10.20537/vm160312
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Received
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17 May 2016
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Language
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Russian
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Citation
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Starodumov I.O., Pavlyuk E.V., Abramov S.M., Klyuev L.V., Galenko P.K., Alexandrov D.V. The effectiveness of parallelizing an algorithm of the PFC equation solution using PetIGA library, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 445-450.
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References
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- Starodumov I., Pavlyuk E., Klyuev L., Kovalenko M., Medyankin A. Analysis of the efficiency PETSc and PETIGA libraries in solving the problem of crystal growth, CEUR Workshop Proceedings, 2015, vol. 1513, pp. 109-122.
- Galenko P., Danilov D., Lebedev V. Phase-field-crystal and Swift-Hohenberg equations with fast dynamics, Physical Review E, 2009, vol. 79, issue 5, 051110, 11 p. DOI: 10.1103/PhysRevE.79.051110
- Galenko P.K., Elder K.R. Marginal stability analysis of the phase field crystal model in one spatial dimension, Physical Review B, 2011, vol. 83, issue 6, 064113, 8 p. DOI: 10.1103/PhysRevB.83.064113
- Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 2005, vol. 194, issues 39-41, pp. 4135-4195. DOI: 10.1016/j.cma.2004.10.008
- Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric analysis: toward integration of CAD and FEA, Wiley, 2009, 360 p.
- Bueno J., Starodumov I., Gomez H., Galenko P., Alexandrov D. Three dimensional structures predicted by the modified phase field crystal equation, Computational Materials Science, 2016, vol. 111, pp. 310-312. DOI: 10.1016/j.commatsci.2015.09.038
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Full text
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